
Class. 
Book 

COPHUGHT DEPOSIT. 



EDUCATIONAL GUIDANCE 

AN EXPERIMENTAL STUDY IN THE ANALYSIS 

AND PREDICTION OF ABILITY OF 

HIGH SCHOOL PUPILS 



BY 

TRUMAN LEE KELLEY, Ph.D. 

Consulting Pyschologkt, Culver Military Academy 



TEACHERS COLLEGE, COLUMBIA UNIVERSITY 
CONTRIBUTIONS TO EDUCATION, NO. 71 



PUBLISHED BY 

^earijcrs College, Columbia Qlmbersfttp 
NEW YORK CITY 

1914 
Monograph 



VV 3 

v o>V 



Copyright 1915 

By 

TRUMAN LEE KELLEY 



MP 



MAY -7 ISte 

©CI.A410135 



PREFACE 

The task of giving tests, establishing averages, and calculating 
relations, which shall serve as a basis for prognosis of mental 
ability, is, in every sense, a social undertaking, and it is only 
because of the kindly cooperation of the principals, teachers, 
and pupils of the two schools studied that it has been possible 
to secure the data that supply the material for this investigation. 
The evaluation of the data has equally been a social task and I 
am particularly indebted to Professors E. L. Thorndike, S. S. 
Colvin, and H. A. Ruger for assistance in grading the preferences 
of pupils in the interest test as to vocations, sports, and enter- 
tainments, and to Mrs. Grace Osgood and Miss Grace Kelley for 
the unique assistance which, as librarians, they were able to 
render in grading magazines and books. 

To the ever-ready, stimulating criticisms of Professor Thorn- 
dike, I am peculiarly indebted, for it is due to his encouragement 
that the investigation covers the three fields of mathematics, 
English, and history instead of one only, and that the number 
of relations determined is as extensive as it is. The field covered 
gives the work whatever of value it has, but the accomplishment 
of it and its appearance in print at this time has been possible only 
because of the devoted and untiring assistance, in grading, 
calculating coefficients of correlation, and deriving regression 
equations, rendered by my wife. 

September, 1914. T. L. Kelley. 



CONTENTS 

SUCTION PAGE 

1. Statement of the Problem 1 

2. Method and Specific Object 4 

3. Elementary School Grades and Their Significance as Evi- 

dence of High School Efficiency 7 

4. Teachers' Estimates and Their Significance 14 

5. Special Tests and Their Significance 19 

Algebra Test 19 

Geometry Test 22 

English Test 25 

History Test 33 

Interest Tests 40 

Grading of the interest tests 44 

Two kinds of reliability coefficients 53 

Grade for entire interest test 55 

Combination of Grades of Various Tests for Purposes of Prog- 
nosis 62 

M ot — Combination of tests with reference to (a) algebra 

and (b) geometry 63 

E ot — Combination of tests with reference to English 64 

H c t — Combination of tests with reference to History 64 

M„i — Combination of the interest tests with reference to 

mathematics 65 

E i — Combination of the interest tests with reference to 

English 65 

H c i — Combination of the interest tests with reference to 

History 66 

M o — Combination of M ot and M c j 66 

E c — Combination of E ot and E oi 67 

H c — Combination of H ct and H c i 67 

Use of Regression Equations 67 

6. Use of all Sources of Data in Estimating Probable Average 

Standing 71 

7. The Age of Pupils as a Factor 73 

8. Comparison with Other Studies 74 

9. Practical Application in High School Classification 81 

10. Guidance Methods 84 

11. Appendix 

Ages of Pupils 86 

Assignment of Numerical Magnitudes for Literal Grades 86 

Extent of error in averaging literal grades 88 

Elementary School Grades 89 

Teachers' Estimates and Combinations of the Same 92 

Bearing of the various factors upon M, E and H 94 



vi Contents 

SECTION PAGE 

11. Appendix — Continued. 

Grading of the Algebra Teat 95 

Derivation of formulae 96 

Grading of the Geometry Test 97 

Grading of the English Test 98 

Grading of the History Test 99 

Bearing of the Various Tests upon Mathematics 99 

Bearing of the Various Tests upon English 100 

Bearing of the Various Tests upon History 100 

Interest Tests — Grading of Books 101 

Grading of Interest Tests with Reference to (a) English, (b) 

Mathematics, (c) History 101 

Combination of Parts of Interest Test with Reference to (a) 

Mathematics, (b) English, (c) History 103 

Combination of Mathematics Tests with Reference to Mathe- 
matics. Similar Combinations of English and History Tests 105 
Combination of all Sources of Data with Reference to Average 
Class Standing 106 

12. Table Giving Original Data 107 



EDUCATIONAL GUIDANCE 



SECTION 1.— STATEMENT OF THE PROBLEM 

Humanity's unvoiced plea for guidance is the foundation of 
all professions. The doctor, the lawyer, the minister find that 
belief and obedience are more often the result of need than of 
understanding and conviction. The modern idea of education 
is crystallizing into an effort to guide rather than to instruct — to 
answer to a need rather than to cater to a curriculum. The 
growing recognition of the need for vocational and educational 
guidance is resulting in the establishment of bureaus endeavoring 
to give the former, and in the training of psychologists to solve 
the problems of the latter. 

The movement for vocational guidance is in its infancy, but 
it only depends upon improved methods and more extended 
research to give it a place with the older professions. Vocational 
guidance has sprung up out of two needs — the need of the em- 
ployer for efficient clerks, mechanics, and laborers and, still more 
important, the need of the individual to utilize his talents to the 
best advantage in order to cope with present-day industrial con- 
ditions. 

This latter demand is most pressing at the time that the 
individual is about to leave school, and it is at this point that the 
major efforts of vocational guidance bureaus have been expended; 
but even a hasty consideration will show that the guidance 
exercised is tardy. It should have been present when the school 
training of the individual became different from that of other 
individuals — when he began to specialize and train himself for 
his life work. It may be stated with assurance that in all cases 
this specialization should be well under way before the completion 
of the formal education of the pupil. 

These remarks suffice to make apparent the need for such 
educational guidance in the high school and college, as shall 
precede and serve as a basis for the later vocational guidance. 
2 1 



2 Educational Guidance 

The general method to determine the accuracy of guidance is the 
same, whether the guidance be educational or vocational, and 
it is one of the chief aims of this study to determine accurately 
the reliability of the estimation of academic capacity. The data 
necessary for accomplishing this are at hand, for high school 
records of academic accomplishment are universally kept. Com- 
parable vocational records are generally not available; but for 
the determination of the reliability of an estimate of vocational 
fitness they are essential, and whenever available the method 
here used is applicable. 

The two chief factors entering into the problem of efficient 
guidance are, first, a correct understanding of the demands of 
prospective tasks and, second, an accurate valuation of the ability 
of the person in question to meet these demands. These two 
main elements of the problem may be stated as requiring an 
analysis of the individual to determine his characteristics, and 
an analysis of the needs of the situation to see to what extent 
the individual meets these needs. This is a general statement 
of the problem applicable to all kinds of guidance. The problem 
here undertaken is termed one in educational guidance, since the 
data concern high school pupils and high school subjects; but 
the method, which is that of calculating the correlation between 
the estimate of a person's fitness for a task and his later perform- 
ance in it, is of general validity and importance and will inevitably 
be used extensively in vocational guidance. 

As success usually depends upon several factors, partial corre- 
lation and the regression equation method are essential in the 
evaluation of the data. This method will be explained more 
fully later. The writer is not aware that it has been used before 
in a guidance problem, but its peculiar adaptability to a problem 
of this nature insures its extended use in the future. 

More specifically, the endeavor of this study is to predict with 
a known, and as high as possible, degree of accuracy the capacity 
of the pupil to carry a prospective high school course. In doing 
this, an analysis of the factors which make for success in the 
course is obtained. The essential objects of the study are thus 

(1) a measurement of the characteristics of the pupil, together 
with the determination of the extent to which these character- 
istics correlate with scholastic ability along certain lines, and 

(2) an analysis of the demands of certain high school courses. 



Statement of the Problem 3 

To illustrate the intimacy of these two problems it may be 
pointed out that if all the essentials of fitness needed to fulfill a 
certain task were known, and if the abilities of the person under 
consideration were completely known, then prediction and 
performance would agree perfectly; and to the extent that this 
condition is approximated, the correlation between prediction 
and performance is increased. 



SECTION 2.— METHOD AND SPECIFIC OBJECT 

When selective classification of a prospective high school 
pupil is attempted, the usual question asked is, what is his general 
mental ability, and he is classified according to the answer to 
that question. The present study attempts to answer that 
question by considerations based upon one of three sources of 
data: (1) the pupil's grammar school record, (2) estimates of 
previous teachers of the pupil, and (3) grades obtained in special 
tests given the pupil at the very beginning of the school year. 
Beyond this, it is imperative, in rendering the most valid decision 
as to the pupil's capacities, that account be taken of his specific 
interests and peculiar genius. An excellent student of mathe- 
matics may be a very poor English scholar, and though this sit- 
uation is not true in the majority of cases, yet the number of 
cases in which it is true is sufficiently great that very material 
injustice will be worked if it is not taken into consideration. 

The further aim of this study is, therefore, to determine, before 
courses in the high school are taken, what the probable ability 
of the pupil in question will be in them. Instead of attempting 
to cover the field of high school work exhaustively, three subjects 
— mathematics, English and history — have been selected for 
study. The general method of procedure with all three subjects 
and all three sources of data is to separate the data into ele- 
ments that are, as far as possible, independent of each other, 
e.g., the teachers' estimates of the pupil are four in number, (1) 
intellectual ability, (2) conscientiousness, (3) emotional interest 
in his work, and (4) oral expression. All of these factors are 
important for scholastic work and it would be desirable if they 
were totally uncorrelated with each other. The first and fourth 
and the second and third are rather closely related with each 
other, but even so there is sufficient independence between the 
four to make their combined significance as indicators of scho- 
lastic success considerably greater than that of a single estimate, 
such as that of intellectual ability. 

If the grades received, or marks given, in the original data are 
represented by X x , X 2 , Xz, X i} and if the grades received in the 
high school mathematics, English and history courses six months 
4 



Method and Specific Object 5 

or a year after the original data are obtainable are represented 
by Xji, Xe, Xh, then the problem is to establish the correlation 
between Xm and the combined measures based upon Xi, X 2 , X 3 , 
X i} and similarly with X E and X H . Expressed as an equation 
it is Xu = Co-\-CiXi-\-c 2 X2-\-CsXz-\-CiXA. This is equivalent to say- 
ing that a certain constant times the grade received in the first 
trait (or test), plus a second constant times the grade received in 
the second trait (or test), plus, etc., gives the probable grade in 
the course about to be taken. The statistical problem involved 
is the determination of the constants c , c h c 2 , c 3 , c 4 , so that the 
Xm values obtained differ on the whole, and when every indivi- 
dual is taken into account, from the actual Xm values by the 
smallest amount possible. 1 

The equation which fulfills this condition is called a regression 
equation, and the constants ci, c 2 , c 3 , Ci, are called regression 
coefficients. They are functions of the coefficients of correlation 
between the various X's and the standard deviations of the X's. 
The theoretical proof of the derivation of these constants may 
be found in Yule, "Introduction to the Theory of Statistics," 
and a considerable amount of the purely mathematical work 
involved in their calculation is given in the Appendix of the 
present work. 2 For an understanding of this investigation (ex- 
cept the Appendix) and the use of the method, it will suffice if the 
reader has well in mind the fact that the value X# for each 
individual obtained by this equation is the most probable value 
which it is possible to obtain from the data X h X 2 , X 3 , Xi 3 . 

This regression equation is the means of prognosis, and to use it 
in the case of any individual it is only necessary to substitute the 
values Xi, X 2 , X s , Xi, for that individual, to obtain a value Xm- 

In addition to knowing the value X M , it is essential to know 
the probable error of it, or to know its standard deviation. This 
has been calculated in all cases, that the reliability of the prog- 
nosis may be known. This reliability depends upon two factors, 
the reliabilities of Xi, X 2 , X 3 , Xi, and the extent to which these 

1 Or, more accurately, that the calculated X M 's differ from the actual 
X M y B by such amounts that the sum of the squares of the differences is a 
minimum. 

2 The writer is about to publish tables which will greatly facilitate the 
calculation of regression equations. 

3 For the mathematician the words "in case the regression is rectilinear" 
may be added. 



6 Educational Guidance 

X's are correlated with Xm (this latter is in part dependent upon 
the former). The reliability of any given measure Xi is given 
by the reliability coefficient, 1 which is simply the value of the 
coefficient of correlation between the given set of Xi's and a 
second set similarly derived. To obtain this measure it is neces- 
sary to have the Xi grades assigned by at least two judges, which 
procedure has been followed throughout except where impossible 
because of the nature of the data, or where totally unnecessary 
because the grading was so completely defined that the judge had 
little or no option left to him in his grading. The formula giving 
this reliability coefficient of a grade, which is the average or sum 

nr 

of the gradings of n judges, is 7~7 77" where r is the correla- 

l + (n — l)r 

tion between gradings of different judges. Most of the tests in 
this study have been graded by two judges, so that the formula 

2r 
becomes — — 
1+r 

It is later explained at some length that the use of correlation 
coefficients, corrected for attenuation, is not permissible in this 
problem. The attempt here is to prophesy accomplishment by 
measuring an existing, not an imaginary, relationship, whereas, 
in the studies using methods for "correcting" raw coefficients 
of correlation, the attempt is to obtain a coefficient which is an 
estimate of an ideal relationship and which does not represent a 
correlation between existent data. This distinction should be 
clearly borne in mind and comparison should not be made with 
studies using coefficients corrected for attenuation. 

In addition to being the means of prognosis, the regression 
equation serves one other important function: the regression 
coefficient C\ gives the weight that must be attached to the 
measure X\, independent of and free from any relation it may have 
with X 2 , X 3 , Xi. It therefore makes it possible to consider the 
importance of each of the factors X\, X 2 , X 3 , X 4 , independent 
of the others. Such an analysis is essential in arriving at the 
separate factors which go to make up efficiency in any given sub- 
ject. This latter use of the coefficients of the regression equation 
will be more apparent when treating of teachers' estimates and 
the special tests, than in the following section covering the use 
of elementary school grades as indicators of high school ability. 

1 See Brown, Mental Measurement, pp. 101-102. 



SECTION 3.— SCHOOL GRADES AND THEIR SIGNIFI- 
CANCE AS EVIDENCE OF HIGH SCHOOL 
EFFICIENCY 

The data here treated consist of the scholastic records of 59 
pupils whose grades were available from the fourth grade through 
the first year of the high school. These pupils had attended the 
same school without a break, except for minor illness in certain 
cases, during this period. The grades of the pupils in the follow- 
ing subjects were copied from the high school records: Fa (first- 
year average grade), Fm (first-year mathematics-algebra), Fe 
(first-year English), 1 7a (7th grade average grade), 7m (7th grade 
mathematics-arithmetic), 7e (7th grade English), 7h (7th grade 
history), 6a, 6m, 6e, 6h, 5a, 5m, 5e, 5h, 4a, 4m, 4e, 4h. 2 

The coefficients of reliability of these measures are not avail- 
able, but they are probably not less than .80 for Fa, 6a, 4a, and 
not less than .75 for 7a and 5a. It was first determined what 
connection there is between 7a, 6a, 5a, 4a, and Fa. In order to 
determine this the correlation between each one of these grades 
and all the rest is necessary. These correlations are given in 
the following table: 

Fa 7a 6a 5a 

7a .719 

6a .728 .730 

5a .531 .425 .541 

4a .624 .551 .573 .576 

There are several surprising items in this table. All of the 
correlations involving 6a and 4a are higher than would be ex- 
pected from the balance of the data. It certainly would not be 
expected that 6th grade marks would correlate more highly with 
first year standing than 7th grade marks, nor that 4th grade 
marks would correlate more highly with first year and 7th grade 
marks than 5th grade marks. It is possible that the teachers of 
the 6th and 4th grades were more expert in estimating the ability 

1 See Appx., pp. 108-116. 

2 See Appx., p. 116. 



8 Educational Guidance 

of their pupils than were the teachers in the 7th and 5th grades. 
However this may be, to get the most out of these particular 
data in their bearing upon Fa, the regression equation, based 
upon these coefficients of correlation and the various standard 
deviations, must be obtained. Calculation shows it to be as 
follows: 1 C • Fa = 1.67 (7a) + 1.3 (6a) + .4 (5a) + .7 (4a). (In 
which C is some constant.) Calculation shows the correlation 
between the Fa's thus obtained, and the Fa's actually obtained 
in the first year to be .789, with a probable error of .032. This 
correlation will be designated by the symbol r FA( 7 >6 ,5,4A)- This 
is a high correlation for data so far apart in time, and the 
division of pupils in the high school into sections according to 
ability, upon the basis of this prognosis, would be much more 
accurate than that which would be possible after observing the 
progress of the pupil in the high school for half a school year; for 
this correlation is undoubtedly higher than that between average 
half-year term grades. Especially would this be true if succeed- 
ing term grades were given by different instructors. 

The argument that this correlation is not perfect and would 
work injustice in certain cases is utterly impotent if the alterna- 
tive is the present very common system of mixing the good, the 
medium and the poor all together, thus actually doing injury 
to all. For any high school having more than a single section 
of each class, and where grammar grade records are available, 
the desirability of classification upon the basis here worked out 
will be apparent, whether considered from the standpoint of the 
nervous strain upon the teachers of a non-homogeneous class, 
from the standpoint of economical administration, or from the 
standpoint of the accomplishment of the pupil. In this connec- 
tion it should be mentioned that the accuracy of a classification 
based upon the marks received in the 7th grade alone is not very 
materially less than that which is based upon the marks from the 
4th to the 7th grades, and would be of very decided value in 
case more extended records are not available. 

There is one drawback to the use of the above regression equa- 
tion, viz: by its use that pupil, who is particularly capable in 
some one line, is not classified more highly in that line than he is 
in others. A more detailed estimate of ability is desirable and 



1 See Appx., p. 91. 



School Grades and High School Efficiency 9 

can be obtained by calculating the regression equations to esti- 
mate ability in the various subjects of the first-year class, instead 
of one regression equation to estimate average high school ability. 
The most probable grade in first-year mathematics (Fm) 
would be determined from the grades received in the different 
elementary school subjects for the years for which the data are 
available, i.e., the most probable value of Fm is equal to some 
combination of 7m (7th grade mathematics), 6m, 5m, 4m, and also 
7e (7th grade English), 6e, 5e, 4e, and so forth for the balance 
of the elementary school curriculum. The grades in only three 
elementary school subjects, mathematics, English and history, 
were taken from the school records (it is the average of these 
three that give the grades 7a, 6a, 5a, 4a), since these subjects all 
run through the last four years of the elementary school, and 
since the means of the various grades for these subjects could be 
determined with considerable accuracy, probably very much 
greater accuracy than with such subjects as nature study, writing, 
music, etc. Furthermore, Fm is undoubtedly more especially 
dependent upon the grades 7m, 6m, 5m, 4m, than upon grades in 
other subjects in the curriculum, and similarly with Fe and 7e, 
etc. It may also be stated that for purposes of determining the 
difference of capacity of a pupil for mathematics and his capacity 
for English there is very little gained by involving a subject such 
as history in the calculation. For these reasons, the bearing of 
7m, 6m, 5m, 4m only upon Fm has been obtained, and in doing 
this it was assumed that the importance of the various years of 
the elementary school was the same as in the case of the average 
first year standing and the average standings of the elementary 
grades. The equation of relation (the term regression equation 
is reserved for equations satisfying entirely the conditions laid 
down for such equations) is therefore as follows: 

C-Fm = 1.67(7m) + 1.3(6m) + .4(5m) + .7(4m) 
Similarly C ■ Fe = 1.67(7e) + 1.3(6e) + .4(5e) + .7(4e) 

The correlation between the Fm's thus obtained and the actual 
Fm's is .580 (r Fll (7> 6> 5> 4ll) ). For English r^ (7> 6 , 5> ^ = .710. The 
greater correlation in the case of English than in the case of 
mathematics may be partly due to an intrinsic difference in the 
laws of development of an individual with reference to these two 
subjects, but it is, at least in part, due to the greater reliability 



10 Educational Guidance 

of the English elementary school marks, since these measures are 
an average of the grades given in two English courses, whereas 
the arithmetic grades are obtained from but a single course. It 
is evident that there is also a greater content difference in passing 
from arithmetic to algebra than in passing from 7th grade English 
to first-year English. From a statistical point of view it does 
not seem likely that the difference in reliability could entirely 
account for the difference in correlation, and the author will 
state that the mathematical probability of the difference being 
due to chance is small, though he cannot express this probability 
in exact numerical terms. 

It has been stated that the value of these coefficients of corre- 
lation lies in their power to differentiate between the ability of 
the pupil in mathematics and in English. The extent to which 
they perform this task in differential diagnosis can be measured 
by comparing for each individual the difference between the 
estimated ability in mathematics and the estimated ability in 
English with the actual difference of ability as shown by the 
grades in the two subjects. If individual (1) is estimated to be 
.7 sigma (standard deviation) above the average in mathematics 
and .4 sigma above the average in English, and the actual grades 
which he received are .9 sigma above the average in mathematics 
and .6 sigma above the average in English, then the estimated 
difference between the abilities in the two subjects is equal to the 
actual difference. 

The extent to which differences in estimation correspond to 
differences in first-year grades is given by the coefficient of 
correlation between these two differences, r(p M _ E ) (7 ? 6i 5> ± t M _ B ). It 
is evident that if this correlation equals zero, then English 
grades in the elementary school are as good a basis for estimation 
of mathematics grades in the first-year class of the high school 
as are mathematics grades in the elementary school — in other 
words, intelligence is general, and may be directed by the in- 
dividual with equal result in any direction. On the other hand, 
if the correlation is perfect, 1 then mental capacity is specific and 
specialized to exactly the same extent and in the same manner 

1 For this theoretical consideration, not in the nature of a prognosis, a 
coefficient of correlation corrected for attenuation might be desired, but the 
data for its calculation are not available, nor is it likely that the assumptions 
underlying its derivation (lack of correlation of errors, etc.) would be sound. 
Such correction, if utilized, would increase the correlation found. 



School Grades and High School Efficiency 11 

in the high school and in the elementary school when dealing with 
the same subjects. Calculation shows that r( FM _ B) ( 7i 6> 5, 4, M _ B ) = .515. 

The net conclusion which may be drawn from these four 
coefficients of correlation is, that it is possible to estimate a 
person's general ability in the first year class from the marks he 
has received in the last four years of the elementary school with 
an accuracy represented by a coefficient of correlation of .789; 
and that individual idiosyncracies may be estimated, in the case 
of mathematics and English, with an accuracy represented by a 
coefficient of correlation of .515. 

The method of doing this is the simple one of substitution in 
a regression equation. The regression equation given above 
proved the best for the school from which the data are obtained, 
but it probably would not occur in the usual school that the 
correlations of the 6th and 4th grades would be relatively as high 
as in this particular school. Assuming that for the usual school 
there is a progressive gain in correlation with first-year standing 
as one proceeds from the 4th to the 7th grade, we would have 
correlations about as follows: 1 

4a 





Fa 


7a 


6a 


5a 


7a 


.67 








6a 


.58 


.67 






5a 


.53 


.58 


.67 




4a 


.50 


.53 


.58 


.67 


<rS 


0"Fa 


* 0"7a 


0"6a 


0-5* 



0"4a 



The regression equation based upon this table is as follows: 
Fa = .4616^ (7a) + .1458 ^ (6a) + .0910 ^ (5a) 

°7k V °Sa 

+ .1094^ ( 4a ) (a) 

In incase the o-'s are all equal this equation becomes, to a very 
close approximation, 

54.9 (Fa) = 25 (7 a) + 8 (6a) + 5 (5a) + 6 (4a) (b) 

Equation (a) is the equation recommended for use in the ordi- 
1 See Appx., pp. 91-92. 



12 Educational Guidance 

nary school system. The elementary student of statistics can 
use this equation without difficulty. First calculate the standard 

deviations, o> A , aikj <r 6A) <t 5a) a^ } then express (.4616—1 as a 



a, 



7a 



a F A 



single number, and do similarly with ( .1458 — - I, etc. This will 

result in an equation of the type (b) except that the coefficient 
of Fa is unity. It then only remains to substitute the values 
7a (the average grade expressed as a deviation from the mean), 
6a, 5a, etc., for each individual considered, to obtain the probable 
grade, expressed as a deviation from the mean, of the individual 
in his high school work. A similar procedure may be followed 
for each high school subject, substituting for 7a, 6a, 5a, 4a, the 
corresponding 7th, 6th, 5th, and 4th grade marks in the subject 
in question. The result thus obtained will give the relative dis- 
tribution of the pupils, but in this latter case the most probable 
mark for the first-year grade may be expected to be numerically 
a little smaller than the grade given by substitution in the equa- 
tion. 

This amounts to saying that the weighting of the grades of the 
various years of the elementary school is probably the same 
whether one deals with average grades or with grades of certain 
subjects, but that the correlation found is probably smaller in 
the latter case than in the former. The essential problem is to 
divide the pupils into groups according to ability, and this the 
values obtained by substitution in the equation will do with 
considerable accuracy. The exact degree of accuracy can be de- 
termined at the end of the school year by calculating the coeffi- 
cient of correlation between the prophesied grade and the grade 
actually obtained by the pupil, due allowance being made for 
difference in the rigidity of grading in the various sections of the 
same course — such differences undoubtedly being present if the 
sections have been divided upon the basis of ability. 

At first glance the fact that in the equation (b) the record in 
the 4th grade is weighted more heavily than the record obtained 
in the 5th grade is surprising. This arises from the fact that the 
4th grade record has a greater independence than the 5th and 6th 
grade records, and therefore contributes more of an independent 
nature upon which to estimate freshman standing. This is to 



School Grades and High School Efficiency 13 

say that from the 4th, 6th and 7th grade records a closer estimate 
of the 5th grade record can be obtained than can be obtained of 
the 4th grade record from the 5th, 6th and 7th grade records. The 
relatively greater independence of the first and last terms of the 
series is to be expected, and is a cause of their greater weighting. 
Before leaving this subject, it is interesting to note that the 
correlation between the average first-year standing and the 
average marks for the 4th grade is .624. This high correlation, 
together with the fact that those who skipped grades were graded 
high by giving them the grades of the preceding year, 1 instead of 
being graded low by giving them the grade of the following year, 
on the ground that having missed a year they would be handi- 
capped in all their succeeding work, is strong evidence that 
natural capacity is a very much more important factor than 
training in determining relative scholastic standing. Indeed, it 
seems that an estimate of a pupil's ability to carry high school 
work when the pupil is in the 4th grade may be nearly as accurate 
as a judgment given when the pupil is in the 7th grade, for the cor- 
relation in the former case is .62 and in the latter only .10 higher. 



1 See Appx., p. 89. 



SECTION 4.— TEACHERS' ESTIMATES AND THEIR 
SIGNIFICANCE 

Toward the close of the first half year the teachers in School A 
were given lists of pupils in groups 1, 2, and 3 and asked to grade 
the pupils according to intellectual ability (I. a.) on each list 
1, 2, 3, etc., as far as valid judgments could be made. Then, 
beginning with the weakest, pupils were to be graded a, b, c, etc., 
as far as judgments could be made. Finally, the remainder of 
the pupils known to the teacher were to be marked M, signifying 
a medium group. The demand that ranking be from the best 
to the poorest, without a medium group, would probably have 
resulted in less accurate judgments throughout the entire series, 
for it would have been beyond the power of the majority of teach- 
ers to have made valid distinction throughout this range. As it 
was, on the average, about 25 per cent were placed in the medium 
group. These rankings were then expressed as deviations from a 
mean and the results of the gradings by the various teachers 
combined for each pupil into a single measure. 1 

The same procedure was followed for the traits conscientious- 
ness (Cons.), emotional interest in school work (Emo. i.), and oral 
expression (Exp.). 

These estimates were obtained before the time of the English 
and history courses used in this study and before the second half 
year of the mathematics courses used. None of the estimates 
used were from the mathematics instructors of the pupils. A 
further effort was made to eliminate the possibility of the esti- 
mates of the teachers being more highly correlated than a chance 
selection of teachers' estimates would yield, by excluding the 
estimates of English and history teachers who later had the same 
pupils, in courses here utilized, that they had already taught in 
the first half year's work. This was possible in all the 460 cases, 
except in the case of 23 estimates which it was necessary to use 
in order to secure sufficient data. 2 The teachers' estimates are 



1 See Appx., pp. 92-93. 
4 See Appx. p. 93. 
14 



Teachers' Estimates and Their Significance 15 

therefore practically free from any direct bearing upon mathe- 
matics, English and history, but there is a certain amount of 
direct connnection with average class standing. For example, 
the estimate of a teacher of Latin, made near the close of the first 
half year of school, enters into the teachers' estimate grade, and 
the grade given by this same teacher for the yearly grade in Latin 
of the pupil enters into the average grade for the year. This lack 
of entire independence operates to slightly raise the correlation 
between teachers' estimates and average class standing. From 
the data at hand this increase is estimated to be less than .03. 

The correlation between gradings by different teachers of the 
same pupil for the same trait are as follows: 

'"(I. a. according to one teacher's estimate) = • ■"Q 
" " " a second " 

'"(Cons, according to one teacher's estimate) -"° 
" " "a second " 

'"(Emo. i. according to one teacher's estimate) ■**■* 
" " a second " " 

'(Exp. according to one teacher's estimate) •■^" 
" " a second " 

On an average there were about two and one-half estimates per 
pupil, so that the reliability coefficients of the various gradings 
are: 

Reliability coefficient of I. a. grading =.493 
" Cons. " =.605 
" Emo. i. " =.505 
" Exp. " =.529 

The conditions laid down for securing teachers' estimates were 
simple to use, but at the same time allowed for as detailed judg- 
ment as possible. When first-class teachers can estimate intel- 
lectual ability with a reliability of only .29 it lessens the confidence 
that can be placed in such estimates of ability and conclusions 
drawn from studies depending upon them. 

Teachers' estimates of pupils have the unique value of indi- 
cating, more or less accurately, single mental traits instead of a 
complex of traits such as are involved in the securing of a grade 
in a subject, but it is highly desirable that these estimates be 
made by several competent individuals, otherwise the measures 
are very unreliable. 



the various 


estimates i 


Av. 


I. a. Cons, 


I. a. .72 




Cons. .62 


.61 


Emo. i. .58 


.61 .66 


Exp. .63 


.82 .55 



.59 



16 Educational Guidance 

The correlations between the various estimates and the 
average grade (Av.) of each 

pupil are given in the ac- Ay L a Cons EmQ { 

companying table. The re- 
gression equation based 
upon this table is: 

c - Av. = 8 I. a., +4 Cons., 
+2 Emo. i., 
+1 Exp. 1 

The correlation between average class standing and the regres- 
sion equation combination of the estimates of traits 

**Av. (I. a., Cons., Emo. i., Exp.), = .7o. 

With such a high correlation, a division of pupils into classes 
by means of teachers' estimates would be highly reliable. The 
use of the equation to estimate probable class standing for a 
school system with a different system of marking from that of 
the schools here considered follows the same general lines as in 
the case of elementary school grades. (See Appendix.) 

In so far as all high school subjects are equally dependent upon 
the traits, intellectual ability, conscientiousness, interest and 
expression, classification according to grading in them is not 
selective. The extent to which these factors have a common 
importance for different subjects can be measured by calculating 
the regression equations involving class standing in different 
subjects and the teachers' estimates. The following equations 
give the regression of mathematics, English, 2 and history, respect- 
ively, upon I. a., Cons., Emo. i. and Exp. For simplicity, all 
standard deviations are assumed equal. M t . e . stands for the most 
probable mathematics grading, based upon teachers' estimates. 
E t . e . and H t . e . have similar meanings. 

M t . e . = .460I.a. + .114Cons. + .129Emo.i.-.014Exp. 

»"MM t e . = -61 

E t . e . =.336I.a. + .251 Cons. +.068 Emo. i. + . 083 Exp. 

r E E t . e . = .64 

H t . e . = .450 1, a. - .024 Cons. + .305 Emo. i. - .287 Exp. 

r H H t . e =.46 



1 See Appx., p. 94. 

2 See Appx., pp. 94-95. 



Teachers' Estimates and Their Significance 17 

The negative significance of expression in the case of mathe- 
matics and history is probably entirely due to the lack of inde- 
pendence of the estimates of oral expression. This is the most 
objective of the four traits and for that reason it might be con- 
sidered the easiest to estimate. This view seems incorrect, for 
oral expression is probably a trait which teachers do not think 
much about and which they make little attempt to measure, with 
the result that, when called upon to give an estimate of it, they 
rely upon associated characteristics, such as intellectual ability, 
conscientiousness and interest, traits already evaluated in their 
minds. The result of such a procedure is to obtain measures of 
expression which are correlated to an unwarrantable degree with 
more fundamental traits. The tendency to rely upon secondary 
criteria in the estimation of mental traits is a very difficult one to 
overcome and the intercorrelations between the four traits esti- 
mated are probably all higher than would be shown to be the case 
with more accurate measurement of them. 

The effect of unwarrantably large intercorrelations upon the 
regression equation is to tend to give the factor which is the 
dependent one, e. g., in this case expression, small or negative 
weighting. The weighting which the regression equation gives 
is the best available for the measure, but the measure is probably 
not at all an accurate one of the trait considered. A reference 
to the table on page 16 shows surprisingly high correlations be- 
tween expression and the other traits. This is itself an indication 
that the measures called "oral expression" are dependent com- 
plexes of other more fundamental traits. 

The equations show a decided variation in importance of the 
different traits with reference to different subjects. Intellectual 
ability is most important in its bearing upon mathematics and 
least important in its bearing upon English. Conscientiousness 
is most important in its bearing upon English and least in its 
bearing upon history. Interest is most important in its bearing 
upon history and least upon English. Expression is the most 
important in its bearing upon English and least in its bearing 
upon history. 

The striking importance of interest for history work, of con- 
scientiousness for English, and of native capacity for mathe- 
matics are points which can be utilized by the teacher giving the 



18 Educational Guidance 

instruction as well as by the person attempting to diagnose 
differentially the pupil's capacities. 

Such estimates of teachers are not proposed as a good basis for 
the determination of the idiosyncracies of pupils, although it is 
possible in a small way to say what study a pupil will be most 
efficient in, simply upon the basis of teachers' estimates of gen- 
eral capacities. The correlation between the differences in math- 
ematics and English grades and the differences in estimate of the 
same is as follows: 

?"(M-E)(M t> e -E t . e .) = -12 1 (Probable error = .05) 

It is therefore apparent that the practical value of such teach- 
ers' estimates as are here used lies, in the main, in their power 
to measure general ability, rather than in a power to indicate 
points of individual strength or weakness. They probably would 
perform much the same function in connection with vocational 
guidance. 



1 Taking into account differences in standard deviations, e.g., by reducing 
all standard deviations to unity. ' 



SECTION 5.— SPECIAL TESTS AND THEIR 
SIGNIFICANCE 

The data here concern the same groups of pupils as in the pre- 
ceding sections dealing with teachers' estimates. Three kinds 
of tests were given to determine ability, interest and preparation. 
We may say that three main factors enter into the production of 
a grade: (1) the mental capacity of the individual, (2) the prepa- 
ration of the individual for the particular course, and (3) the 
effort and interest of the individual in the particular subject. 
The importance of these three factors differs materially for differ- 
ent subjects, e. g., it requires a previous preparation in algebra 
and analytical geometry in order to carry calculus, and it would 
be a very peculiar genius who could read Virgil without previous 
Latin study. In these courses the factor of preparation is of 
prime importance. Courses in English, history, the sciences, 
commercial branches and the like, do not so definitely demand 
a certain accumulated store of knowledge as a foundation. The 
relative importance of these three factors is worthy of extended 
study and the data here given throw but little light upon the 
question. In drawing up tests these three factors were con- 
sidered with rather special emphasis upon the first and third. 
The high school subjects covered are algebra, geometry, English, 
and History, and a description of the various tests will reveal 
the parts devised to measure each one of these factors. 

(A t ) Algebra Test 

The following test (called an algebra test simply because it was 
given to classes just starting in algebra) was devised for the pur- 
pose of measuring the ability and preparation of the pupil for 
algebra. Following each problem are given directions for grading 
it. 

Administration of the test: The only precaution that need be 
indicated in administering the test is that the teacher refrain 
from explaining any of the questions verbally. Question 5, in 
particular, loses its value if the slightest explanation is made. 

19 



20 Educational Guidance 

Algebra Test and Directions for Grading 
For all problems: maximum grade 10, minimum grade 

Name Date 



1. Add: 132 2. Multiply: 

580 42976 

649 30851 

356 

774 
263 
925 
191 
417 
828 

From 10 deduct 4 for each error in addition, or in carrying forward. 
From 10 deduct 4 for each mistake in placing partial products, 2 for each 
mistake in partial product, and 2 for each mistake in addition. 

3. Divide 457219 by 638 and carry answer to one decimal place. 

From 10 deduct 2 for each failure to draw down, 3 for a mistake in decimal 
point, 2 for each error] in subtraction, and 2 for failure to carry work to one 
decimal place. 

4. Simplify: 6f-3|-l|R2J-l|. 

From 10 deduct 2 for each mistake in simplifying a term, 3 for each error 

in addition. 

„. , , K , 33 13 61 , 9 7 

Give a grade ot 5 tor answer — — + 7 — t- 

5 4 40 4 4 

5. Is the square constructed on a line (3+5) eight inches long greater than, 
equal to, or less than, the sum of the squares constructed on lines 3 inches and 5 
inches long? Explain. 

If explanation shows an understanding of the problem grade it 10. Give 
grade of 2 for (8 X8) - (5 X3) =49. 

6. What is that number such that if it is multiplied by itself and added to 
11 the result is 27? 

Give grade of 2 for answer 16. 

7. A certain balloon without its basket will just lift a weight of 160 pounds. 
What is the weight of the balloon and basket if the basket weighs 20 pounds? 

Grade 10 for answer — 140, or for statement " 140 pounds less than nothing," 
or similar statement. Grade all other answers 0. 

8. Simplify: & * | X f + £. 

From 10 deduct 6 for incorrect inversion, or failure to make correct inver - 
eion, 4 for each error in cancelling, and 4 for each other error. 

3_3 

9. Simplify: - — -. 

3 8 
Give credit of 3 for correct simplification of numerator, 3 for denominator, 
and 4 for the balance. 



Special Tests and Their Significance 21 



10. Simplify: 



2 V 11 
3*12 

9 2 



Same as 9. 

11. Find lowest common multiple and highest common factor of 42, 56, 63, 
84. 

Give credit of 2 for all factoring correct, 4 for H. C. F. if plainly labelled 
and 4 for L. C. M. 

12. January 1 of a certain year the temperature was 70 degrees, January 2 
it was 40 degrees. What was the temperature January 3 if it was still colder 
and the difference between the temperatures of January 3 and January 1 was 
three times as great as the difference between the temperatures of January 2 
and January 1? 

Give credit of 2 for answers of 90°, or 20°. 

13. Find a number such that if 5 is added to 3 times that number the result 
is 38. 

Grade 10 or 0. 

14. One-third of a certain number added to 7 is equal to 22. What is the 
number? 

Give credit of 2 for answer of 5. 

The primary purpose of problems 1, 2, 3, 4, 8, 9, 10, 11 is to 
test the thoroughness of the preceding preparation of the pupil. 
The remaining questions are primarily for the purpose of testing 
his capacity to deal with algebraic material; questions 5, 6, and 
12 testing his ability to understand the written statement of a 
problem and to deal with negative magnitudes, and questions 6, 
13, 14 demanding elementary algebra, or at least a process of 
thinking which is very closely related to simple algebraic reason- 
ing. Problem 7 may be objected to on the ground that the stu- 
dent of physics, who has weighed gases and the like, may be 
misled by the term "weight" when a negative magnitude is 
demanded for a correct solution of the problem. None of the 
subjects showed that this particular difficulty was present in their 
minds, probably because none of them were familiar with the 
necessary physics. 

The grading is highly objective and the reliability accordingly 
very high. To calculate the reliability, a sample was graded by 
two judges. The correlation between the total grades for each 
pupil as determined by the two judges, is .996, which is the 
reliability coefficient, as most of the papers were graded by a 
single judge. The various problems in this test are approxi- 



22 



Educational Guidance 



mately l of equal significance and the sum of the grades of all of 
the problems is the grade for the test. To obtain a distribution 
which would be convenient for purposes of calculation from the 
grade thus obtained, the average grade of the group in question 
was subtracted and the remainder divided by 5, keeping the result 
to the nearest integer. This grade is designated by A t (algebra 
test) and when grouped with the grades of the geometry test by 
M t (mathematics test). 

(G t ) Geometry Test 

Administration of test: In giving the following test, problems 
1 and 2 require explanation. A demonstration is given the 
pupils of a simpler problem, to show the nature of the requirement. 

Paper, about one foot square, is held against the black- 
board with the top edge horizontal, folded once from the 
bottom up, a second time from the right to the left and, while 
still close to the blackboard and without rotating the paper, 
a V-shaped notch cut into it. The pupils 
are then asked to describe, orally, the ap- 
pearance of the paper when unfolded and 
after receiving a few correct answers the 
paper, still against the blackboard, is un- 
folded, enabling the entire class to see that 
the unfolded paper does have the shape 

The test question is then given, folding the 
paper along a diagonal, giving it this appearance 
a second fold leaves 
it in this shape 
a third 
in this 






and after notching it appears thus 



The pupils are then asked to represent its appearance when 
unfolded. 

The nature of the requirement in the second question can be 
made clear by means of two large wooden compasses, each hand 
holding points of the different compasses, and demonstrating the 



See Appx., pp. 95-96. 



Special Tests and Their Significance 



23 



lack of rigidity of the diamond-shaped frame thus formed. 
Care should be taken not to indicate the position, or number, 
of braces necessary to make the figure rigid. 



Geometry Test and Directions for Grading 
All problems: Maximum grade 10, minimum grade 



Name. 



Date. 



1. The accompanying diagram represents a square 
sheet of paper which is folded three times by the 
teacher and cut. Draw in the square, in their correct 
position, the holes cut out. 



Credit given for drawings as follows : 
10 8 6 -f- 



M 



o 
o 






V V 

V V 



2. Suppose that AB, BC, CD and DA 
are sticks of wood hinged together at 
points A, B, C and D. How many braces 
are needed to make the figure rigid and 
where would you put the brace or braces? 

For one brace properly placed give credit 
of 10, improperly placed credit of 4. For 
two braces give credit of 2. 

3. John's mother forbids him to leave 
Broadway. James' mother forbids him to 
leave Amsterdam avenue. They are obe- 
dient sons, but are also very fond of seeing 
each other, so how can they meet? 

Give credit 10 for answer 72nd St. Any 
other answer 0. 



4. AB is a railroad track. C is a stake 
to which a cow is tied with a 30 ft. rope. 
DE measures a distance of thirty feet. 
One day the cow, while grazing at the 
end of its rope, is struck by the train. 
Mark the place or places in the diagram 
at which this must have occurred 

Give credit 10 for indicating two points 
correctly, 6 one point, 6 for distance be- 
tween the two correct points. 





24 



Educational Guidance 



5. In the accompanying figure, 
the distance along the circle from 
B to C equals the distance along 
the circle from A to B. Also, the 
straight fine BC equals the straight 
line AB. Does the curved line 
from A to C equal twice the curved 

line from A to jB? 

Does the straight line AC equal 
twice the straight fine AB1 



Give credit 10 for both answers 
correct, 2 for one correct. 




6. What are the areas of figures A, B, and C? A . . 
In what respect, if any, are figures A and B alike? 
In what respect, if any, are figures B and C alike? 
In what respect, if any, are figures A and C alike? . 



.,B. 





c. 



H- 



Give credit: 

1 for A =9, £=4, C=4. 
3 A and B both squares. 

2 A and B alike in shape. 

3 B and C equal in area. 

1 B and C both parallelograms. 
3 A and C both rectangles. 

2 A and C not at all alike. 



x c 
7. Find the value of x from the equation - = -. 

a 

a c 
Find value of y from the equation - = -. 

yd 



Give credit: 
4 for x 



be 

d' 



6 for y = 22. 
c 

Anything else 0. 

In the following question, is the third statement proved if the first two are 
true? Write "proved" or "not proved" after it. 

8. 1. Every chalet is a bungalow. 

2. Jones' house is a bungalow. 

3. Therefore Jones' house is a chalet 

Credit 10 or 0. 

Do the same for the following question : 



Special Tests and Their Significance 25 

9. 1. Every chalet is a bungalow and every building that is not a bungalow 

is not a chalet. 

2. Smith's house is a bungalow. 

3. Therefore Smith's house is a chalet 

Credit 10 or 0. 

Do the same for the following question : 

10. 1. Every building that is not a chalet is not a bungalow. 

2. Brown's house is in no particular different from a bungalow. 

3. Therefore Brown's house is a chalet. 
Credit 10 or 

The primary purpose of all the problems, except problem 7, is 
to test capacity; problem 1 testing ability to image geometrical 
forms and movement. Problems 2, 3, 4, 5, 6, are locus problems, 
and problems demanding a common sense interpretation of 
geometric facts. Problem 7 is a problem to test the pupil's 
previous preparation in the line of ratio and proportion. Prob- 
lems 8, 9 and 10 are problems in logic aimed to test the pupil's 
ability to handle reductio ad absurdum proofs and converse 
propositions. Problem 10 is a difficult problem and is meant to 
tax the most able pupil. It may be said that all the tests were 
devised with a view to securing a good distribution of marks. 
It was desired that the most efficient pupil would just succeed, 
or just not succeed, in making a perfect score, while at the same 
time the tests were meant to be sufficiently easy in places to secure 
the cooperation of the poorest pupil. The reliability coefficient 
for this test is very high, being .994. A number of the problems 
in this test did not prove as significant as conferences with various 
teachers of geometry led the author to expect, 1 and the grade 
for the entire test is taken as the sum of the marks for problems 
1, 7, 8, 9, 10. To obtain a convenient distribution for purposes 
of calculation, from the grade thus obtained the average of the 
group in question was subtracted, and the remainder divided by 
3, keeping the answer to the nearest integer. This grade is 
designated by G t , or M t when grouped with algebra data. 

(E t ) English Test 

The English test which follows, together with the explanation 
of the grading and the sample grading, will explain the purpose 
for which it was devised. It is fundamentally an ability test 
and seems to meet the requirements very well, as none of the 

1 See Appx., p. 97. 



26 Educational Guidance 

pupils gave evidence of familiarity with the subject matter of the 
test. 

Administration of the test: Tell the pupils that you are about to 
read an account of an incident in the life of the founder of one of 
the great Eastern religions and that after reading you are going 
to ask them questions about it. Then read the following: 1 

English Test 

"A woman — dove-eyed, young, with tearful face 

And lifted hands — saluted, bending low: 

"Lord! thou art he," she said, "who yesterday 

Had pity on me in the fig-grove here, 

Where I lived lone and reared my child; but he 

Straying amid the blossoms found a snake, 

Which twined about his wrist, whilst he did laugh 

And tease the quick forked tongue and open mouth 

Of that cold playmate. But, alas ! ere long 

He turned so pale and still, I could not think 

Why he should cease to play, and let my breast 

Fall from his lips. And one said, ' He is sick 

Of poison' ; and another, ' He will die.' 

But I, who could not lose my precious boy, 

Prayed of them physic, which might bring the light 

Back to his eyes; it was so very small 

That kiss-mark of the serpent, and I think 

It could not hate him, gracious as he was, 

Nor hurt him in his sport. And some one said, 

' There is a holy man upon the hill — 

Lo! now he passeth in the yellow robe — ■ 

Ask of the Rishi if there be a cure 

For that which ails thy son.' Whereon I came 

Trembling to thee, whose brow is like a god's, 

And wept and drew the face cloth from my babe, 

Praying thee tell what simples might be good. 

And thou, great sir! didst spurn me not, but gaze 

With gentle eyes and touch with patient hand; 

Then draw the face-cloth back, saying to me, 

'Yea! little sister, there is that might heal 

Thee first, and him, if thou couldst fetch the thing; 

For they who seek physicians bring to them 

What is ordained. Therefore, I pray thee, find 

Black mustard-seed, a tola; only mark 

Thou take it not from any hand or house 

Where father, mother, child, or slave hath died; 

It shall be well if thou canst find such seed.' 

Thus didst thou speak, my Lord!" 

The Master smiled 
Exceeding tenderly. "Yea! I spake thus, 
Dear Kisagotami! But didst thou find 
The seed?" 

"I went, Lord, clasping to my breast 
The babe, grown colder, asking at each hut — ■ 
Here in the jungle and towards the town — 
'I pray you, give me mustard, of your grace, 
A tola — black : ' and each who had it gave, 



1 Taken verbatim from Edwin Arnold, Light of Asia, p. 124-8. 



Special Tests and Their Significance 27 

For all the poor are piteous to the poor; 

But when I asked, ' In my friend's household here 

Hath any peradventure ever died — 

Husband or wife, or child, or slave?' they said: 

'O Sister! what is this you ask? the dead 

Are very many, and the living few!' 

So with sad thanks I gave the mustard back, 

And prayed of others; but the others said, 

'Here is the seed, but we have lost our slave!' 

'Here is the seed, but our good man is dead!' 

' Here is some seed, but he that sowed it died 

Between the rain-time and the harvesting!' 

Ah, sir! I could not find a single house 

Where there was mustard seed and none had died ! 

Therefore I left my child — who would not suck 

Nor smile — beneath the wild-vines by the stream, 

To seek thy face and kiss thy feet, and pray 

Where I might find this seed and find no death, 

If now, indeed, my baby be not dead, 

As I do fear, and as they said to me." 

" My sister! thou hast found," the Master said, 
"Searching for what none finds — that bitter balm 
I had to give thee. He thou lovedst slept 
Dead on thy bosom yesterday : to-day 
Thou know'st the whole wide world weeps with thy woe : 
The grief which all hearts share grows less for one. 
Lo! I would pour my blood if I could stay 
Thy tears and win the secret of that curse 
Which makes sweet love our anguish, and which drives 
O'er flowers and pastures to the sacrifice — 
As these dumb beasts are driven — men their lords. 
I seek that secret: bury thou thy child!" 

The questions to the pupils are as follows: 

(1) State one or two things about the story which you particularly liked. 
(6 minutes.) 

(2) Write an account of the story as fully as you can remember it. (9 
minutes.) (5 minutes for reading the passage, giving a total time of 20 
minutes.) 

The grading was upon the following four points, though the grading upon 
Ev, E a and Ew only, are used in obtaining a single measure of the English 
test: 

Ev Valuation of the essential ideas in the poem. (Grade approximately 

from to 10, with an average of 5. Further explanation follows.) 
Ea Accuracy and extent of description. (Start with 4 and to this add £ 

for each point correctly made and subtract 1 for each point incorrectly 

made.) 
Ew Written expression. (Grade from to 10, with an average of 5. Give 

some slight weight to spelling.) 
Ed Dramatization. (Grade from to 10, with an average of 5.) 

F 1 -4-F 1 I W" 
The reliability coefficient of the English test, — - — - 1 ' 

o 

or E t , equals .969, since the grades used are the sum of the grades 
of two judges and the correlation, based on a sample of 36, 
between the grades given by the judges is .940. 



28 Educational Guidance 

The grading for valuation of the essential ideas of the poem was largely 
based upon the answer to question (1). It followed closely the following 
scheme: 

Grade below: given for selecting the following as the point liked the best: 
10 ±1 Love shown in the Master's way of teaching that suffering is uni- 
versal. 
8 ±1 "The grief which all hearts share grows less for one." 
8 ±2 Appreciation of poetry and language used. 
6 ±1 Master's statement to the mother that the whole world suffers, or the 

idea that suffering is universal. 
5 ±1 Master's statement, "I would pour my blood if I could stay thy 

tears." 
4|±1 "The poor are piteous to the poor." 
4 ±1 Mother's tenderness and love for her child, or the mother's cry that 

she cannot lose her child. 
3 ±1 Mother's trust in the Master, and her courage. 
1 ±1 Honesty and strength of mother in not taking forbidden seed. 

The plus or minus after each grade indicates the amount that quite gen- 
erally is to be added or subtracted, depending upon the answer to the second 
question, as follows: 

Add 1 for genuine appreciation of the Master's character, i. e., his gentle- 
ness, compassion, humanity, and for genuine appreciation of the 
first three points above. 

Add for correct narrative. 

Add — 1 for demonstrated lack of correct appreciation and for incorrect nar- 
rative which betrays incorrect appreciation of the Master's char- 
acter and motive. 

Having grades for accuracy (Ea), valuation (Ev) and written expression 

(W) ( W = Ew + Hw > or the average of the grades for written expression 

* 2 \ 

for the English and history tests / the single grade for the entire test is the 

average of these three grades minus the mean for greater convenience after 
multiplication by two, i. e., Et = f (Ea+Ev+W-mean). 1 

In the following samples, given to illustrate the method of 
grading, the points for which credit in accuracy has been given 
are underscored once and the incorrect points, for which credit 
was deducted, have been underscored twice. The grading for 
dramatization is not used in the final score for the test, but is 
given as it may have some interest in itself and probably has a 
specific significance in some other bearing than upon English. 

1 See Appx., p. 98. 



Special Tests and Their Significance 



29 



Name (Pupil No. 187). 



Date. 



I. I like the story of the poem very much. I think it 
is very pathetic and has a good point — I refer to the 
mothers grief being lessened because she knew all others 
had to suffer. I also like the way the author wrote the 
poem. It is well told, and in beautiful language. 

II. The mother throws herself at the feet of the 
master and says that she come to him to now because 
yesterday he was so kind to her and when on the 
desert her child was playing with a snake and it bit 
him, and she feared for his life, she went to him and asked 
consul of him. He said that she should get mustard seed 
from somebody, but beware not to take it from anyone 
in whose house there has been a death. 

"Yes," says the master, "and did you get the mustard 
seed? " 

"I went into every 
asked for the mustard seed 



hut," 



all 



gave it to me, for 
but when I asked if 



says she, and 
and the good people 
the poor give to the 
there had been a death 



poor 

in the house, they all answered, yes. So now I have 
to you, dear master, to once more seek consul, ere 
my baby dies, if he be not dead already. " 

The consul speaks, "Yesterday when you came to 
me, and asked my aid, your babe was already dead, 
but I let you go and try to get the mustard seed, so 



Hw 

Ew+Hw 



Et = f(Ea+Ev+W-mean 1 ) = §(9+9+4-19) =2.0. 



Grading 



Ea 

4 

.5 
-1 
.5 
.5 

.5 

.5 
.5 
.5 
.5 
.5 
.5 

.5 

.5 


Ev 

8 

1 


Ew 


Ed 


9 


9 


4 

4 

4 


7 



1 For table of means see p. 68. 



30 



Educational Guidance 



Name (Pupil No. 188) . 



Date. 



Grading 



I. I think that the lord was very good and tender 
in telling the mother to find something that was not, 
and telling her that that thing would cure the baby. 
In that way she did not get a shock. 

I think the mother did right by not giving the baby 
the wrong seed, when she could not find the right seed 
and then going to the lord again for advice. 

II. When the story opens; a young mother is 
bending low to a lord of her religeon and tells the fol- 
lowing story: "Yesterday while my child was playing 
in the garden and finding a snake began to play with it. 

The snake bit it leaving a small mark on the child's 

skin and some neighbors said that the baby was dead, 
others that it was not dead yet but was dying of poison. 
And others advised me to go to a certain lord who 
lived over the hill and to ask him what to do to the 
baby to save him and then they told me that the man 
in a yellow robe who was walking on the road by the 
house was the lord so I ran up to him and knelt down 
to salute him and then I took the face cover off his face 
and showed the lord the mark and the lord felt the baby 
and told me to go and get some black mustard seed 
but it must not come from a house wherein a father, 
mother, child or 



Hw 
W 



Et = f (10.5+10+3-19) =3.0. 



Ea 



Ev 



10 



.5 

.5 
.5 
.5 
.5 
.5 



.5 

.5 
.5 
.5 

.5 



E w 



Ed 



10.5 10 



Special Tests and Their Significance 



31 



Name (Pupil No. 200). 



Date. 



Grading 



I. It seems to me that one of the finest points in 
this passage, is the tenderness that runs all through it. 
It is in the mother's speach when she talks of her 
child, and also in the answer, — full of pity and truth. 
Another thing about it is the wording, for the passage, 
although written in prose, sounds almost like poetry 
or music, on account of the beautiful words used. 

II. A woman, with tears in her eyes, came and 
threw herself at the feet of the Master. She told 
him of her child, who, while playing in the garden 
had been stung by a serpent. In a short time he 
grew pale and cold, and people said he would surely 
die. But the mother, unwilling to give up hope, had 
gone to the Master, certain that he, in his wisdom, 
could aid her, and restore her boy to health. And 
the Master, full of compassion , had told her to go 
with her child, from house to house, and beg for 
mustard seed, but from any house where man or 
woman, slave or child had died, she should not accept 
the seed, but go elsewhere. Carrying her child the 
mother had begged at every door, but, although 
glad to give her seed, in every house someone had 
died, so the 



Hw 
W 



Ilia 

4 


Ev 


Ew 


Ed 


.5 
.5 


9 






.5 

.5 
.5 








.5 
.5 








.5 
.5 
.5 


1 






9 


10 


6 

9 
7.5 


6 



E< = §(9+10+7.5-19)=5.0. 



32 



Educational Guidance 



Name (Pupil No. 206). 



Date. 



I. The story is extremely touching. The picture of 
the the "sad tearful face" is most vivid, and the little 
"face so pale and still " can almost be seen. We 
certainly hope that the mother was comforted. 

II. A woman once had a beautiful little child. She 
loved him dearly. The boy would daily sleep on some 
dry grass. One day, the mother being tired and weary, 

(How) 



fell asleep. 



Then came a large venomous 



snake and bit the child, so that he died. And when 
the mother awoke she and saw the still pale face of her 
baby she rent her garments, whilst all the people said 
"There is no hope." But then one man espied the 
doctor of the village. And quickly he spoke, saying 
"There is the doctor! go you to him, mayhap he'll 
give your child to you again." Then on her knees, 
saluting humbly she begged the "wise" man. "My 
daughter, if you wouldst your child recover go you 
from house to house and beg and say "Give me some 
mustard seed" but if there be by any chance a dead 
man in that house, then leave the seed, for is a child 
or man or woman there has died, the charm is broken. 
Go, and if thou succeedest — 



Et = f (3+6+5.5-19) = -3.0 



H w 
W 



.5 
.5 



-1 
-1 
-1 

-1 



.5 



.5 



.5 
.5 



3.0 



Grading 



Ev 



Ew 



Ed 



10 



5.5 



Special Tests and Their Significance 



33 



Name (Pupil No. 124). 



Date. 



I. After the snake bit the child how very sad the 
mother was, and she did every thing to try and save 
him. 

II. The story was about this child that was 
bitten by a snake and he was going to die and the 
mother tried to get some mustard seed but nobody 
had any and the child died. 



Et = f(3 + l+0-15) = -7.3 



Hw 
W 



Grading 



Ea 

4 

.5 

-1 

.5 
— 1 


2 
-1 


Ew 


Ed 


3 


1 








3 



(H t ) History Test 

The history test follows much the same lines as the English 
test. None of the pupils showed evidence of familiarity with 
the subject matter. 

Administration of the test: Draw a map of Italy and Sicily on 
the blackboard, indicating the following provinces and cities: 
Piedmont, Genoa, Venice, Rome, Naples, Calabria, Messina, 
Palermo and Marsala. In addition to these places write the 
names "Garibaldi" and "Victor Emmanuel" on the board. 
Give orally necessary historical groundwork as follows: "Victor 
Emmanuel was the king of Piedmont. (Point out.) He had 
expressed his willingness to lead an insurrection to establish a 
free and united Italy whenever the other states of Italy should 
revolt. The Two Sicilies (point out) and the other small states 
of Italy were governed by rulers who were opposed to a united 
and republican Italy. 

"These are all the facts that you will need to know to under- 
stand the selection about to be read. Remember those points 
that you like and that you consider historically important." 
(Allow 8 minutes for the reading.) 1 

History Test 

"Garibaldi was the hero on the field of battle. The last of knight-errants, 
he was the very incarnation of Romance and Revolution. Bred to the sea, 

1 This selection is a modification of pp. 392-3, 402-4, Sedgwick, A Short 
History of Italy. 
4 



34 Educational Guidance 

he always retained the jaunty, gallant bearing of a mariner. His countenance 
(childlike and honlike) — with its broad tranquil brow, benign eye and reso- 
lute mouth — in youth all sparkling, gradually changed with care and dis- 
illusion, but he still kept the seaman's mien and the seaman's lightsome eye. 
He was the beau ideal of a romantic hero. After his unsuccessful raid into 
Piedmont he had gone to South America, where he lived a wild life of guerilla 
warfare, fighting like a Paladin on behalf of republican revolutionaries who 
were struggling for their freedom. All the time he was training a band of 
Italian adventurers, his legion, so that they should be ready when their country 
had need of them. These men rushed to the defense of the city. Their entry 
was most picturesque. The gaunt soldiers, wearing red shirts and pointed 
hats topped with plumes, their legs bare, their beards full-grown, their faces 
tanned to copper color, with their long black hair dangling unkempt, looked 
like so many Fra Diavolos. At their head Garibaldi, in his red shirt, with 
loose kerchief knotted round his throat, the regular beauty of his noble, 
leonine face set off by his waving hair, mounted on a milk white horse, rode 
like a demigod." 

"A short time after what has just been read the following 
events took place:" 

"In the meantime Francis II, a weak, ignorant, bigoted lad, had mounted 
to the throne of the 'Two Sicilies.' In April, 1860, a revolt began in Palermo, 
and, though suppressed there, spread. Two young patriots, Crispi and Pilo, 
went about stirring the people to action. Garibaldi was begged to put him- 
self at the head of the proposed revolution. On the night of May 6, two 
ships, the Lombardy and the Piedmont, secretly left Genoa, and took Garibaldi 
and a thousand volunteers aboard. This band, known as 'the thousand,' 
is nearly as famous and as legendary as King Arthur and his Round Table. 
On May 11, the ships landed at Marsala. Two cruisers from Naples came up, 
but two English men-of-war happened to be there also; and the English cap- 
tains, under guise of friendly notifications to the Neapolitans, took some 
action which delayed the latter long enough to let the last Garibaldians dis- 
embark. Once on shore Garibaldi's volunteers ran to secure the telegraph 
office. They arrived just after the operator had telegraphed that two Pied- 
montese ships, filled with troops, had come into the harbor; a Garibaldian was 
able to add to the message, 'I have made a mistake; they are two merchant- 
men.' The answer came back, 'Idiot.' The volunteers marched inland. 
A provisional government was organized; Garibaldi was made dictator, and 
Crispi secretary of state. The cry was 'Italy and Victor Emmanuel!' Gari- 
baldi was joined by insurgent Sicilians, and, with numbers considerably 
increased, fought and defeated the Bourbon army. The story reads like the 
exploits of Hector before the Greek trenches. Victory followed victory. 
Palermo fell, Milazzo and Messina; then he crossed the straights and invaded 
Calabria. This marvelous triumph, for there had been thirty thousand troops 
to oppose Garibaldi, frightened King Francis; he proclaimed a constitution, 
but it was too late. Garibaldi swept on victorious, and the king fled from 
Naples (Sept. 6); the next day Garibaldi marched in and assumed dictator- 
ship of the kingdom. 

"Victor Emmanuel took up the cause and, marching south, joined with 
the forces of Garibaldi and together they decisively defeated the opposing 
army. In February, 1861, the first Italian parliament was held and Victor 
Emmanuel formally received the title of 'King of Italy.' Excepting Rome 
and Venice, Italy was free and independent." 

Questions as follows: 

(1) What do you think was probably the next important event? (2 
minutes.) 

(2) Describe the character and appearance of Garibaldi. (4 minutes.) 



Special Tests and Their Significance 35 

(3) Beginning with the departure of Garibaldi and his men from Genoa 
write a detailed account of as much of the story as you have time for. (Bal- 
ance of time — 6 minutes.) 

Each paper was graded upon the following points, though the grading upon 
Ha, only, is used as the measure of the history test. H w is used in connection 
with the English test. 

Hv Valuation — historical forecast and appreciation of the essential his- 
torical facts. (Grade approximately from to 10, with an average 
of 5. Further explanation follows.) 

Ha Accuracy and extent of description. (Start with 4 and to this add 5 
for each point correctly made and subtract 1 for each point incor- 
rectly made.) 

H w Written expression. (Grade from to 10, with an average of 5. Give 
some slight weight to spelling.) 

Hd Dramatization. (Grade from to 10, with an average of 5.) 

The grading for valuation depended in part upon the answer to question 
(1). The grading of this historical forecast followed closely the scheme 
below: 

Grade below: given for selecting the following as the next historical event: 
7±1 Drawing up a constitution. 

6±1 Peaceful acquisition of Rome and Venice. 

5±1 Conquering of Rome, or of Rome and Venice. 

Garibaldi given some honor. 
Establishment of a government. 
4±1 Peace for a short time and then revolts. 

Garibaldi rebels against Victor Emmanuel. 
3±1 Failure to answer. 

2dbl Uprising and revolution by the people. 

Garibaldi made king. 

The plus or minus after each grade indicates the amount that quite generally 
is to be added or subtracted, depending upon the answers to the second and 
third questions. For the second question, 

Add 1, or more, for genuine appreciation of the traits of character which 
were essential to Garibaldi's success. 

Add for correct personal description. 

Add — 1 for incorrect personal description which does injustice to Gari- 
baldi's character, and for irrelevant but correct data, e. g., trip to 
South America. 

For the third question, 

Add 1 for correct references to motive and organization, e. g., "to establish 
a free and united Italy " ; "formed a provisional government"; "joined 
by insurgent Sicilians"; "proclaimed a constitution"; etc. 

Add for correct narrative. 

Add — 1 for incorrect narrative which violates principles involved and for 
misunderstanding of organization, e. g., "Garibaldi sailed to Mar- 
seilles and fought the King of France"; or for attributing incorrect 
motives. 

As already mentioned the accuracy grading H a is the measure for the 
entire test for convenience multiplied by two, i. e., Ht = 2(H a — mean). 1 



See Appx., p. 99. 



36 



Educational Guidance 



The reliability coefficient of H t is .956 since the grades used are 
the sum of the grades given by two judges and the correlation 
between the latter, based on a sample of 36, is .916. 

In the following sample tests, given to illustrate the method of 
marking, the gradings for valuation and dramatization are 
included though they are not used in obtaining the final score 
for the test. 



Name (Pupil No. 226). 



Date. 



I. The next important event might have been the 
taking of Venice and Rome by Garibaldi and Victor 
Emmanuel, making Italy a United Kingdom. 

II. Garibaldi wore a red coat, high hat with a plume 
and boots. His character was a very strong and good 
one. He desired to do good for his country, therefore 
fought well and won many victories. 

III. Garibaldi was a very brave soldier who was 
sent by the King of Piedmont, Victor Emmanuel. He 
and one thousand men Btarted down to the southern 
part of Italy, by water. They reached the most south- 
ern of the two Sicilys, and conquered Palermo first. 
A telegraph had been sent just before their arrival 
and it said that these men were coming to conquer 
them, but as Garibaldi reached there he said "no that 
is not right, we are merchants," so another telegram 
was sent. Garibaldi and his men marched on to 
Marsala and conquered that city. He won victory . . . 

Ht=2(H a -mean) =2(1.5-6.5) = -10.0. 



Grading 



Ha 
4 


H v 


Hw 


Hd 


.5 
-1 
.5 
.5 


5 
.5 






-1 
.5 








-1 








-1 








-.5 


-.5 






1.5 


5 


5 


5 



Special Tests and Their Significance 



37 



Name (Pupil No. 225). 

I. The fall of Rome or Venice which would make 
all Italy independent! 

II. Garibaldi was a seamanlike, strong phisycaly 
and mentaly with a patriotic spirit. He had a 
handsome face, intelligent eyes. Dressed in plumed 
cap, red shirt and loos bandana around his neck he 
looked quite fierce. 

III. It took us only a day to coast down to Palermo 
where we disembarked as quickly as possible while 
to English cruisers held up some of the ships of the 
King of Sicily. We captured the town and assured 
the King of Sicily over telegraph that no such thing 
had happened. We had soon captured all the south- 
ern cities and were marching north to Capture Naples 
but the King hearing of our approach fled. King 
Emanuel came to our help and we soon had all of the 
states except Rome and Venice which we soon expect 
to have. Our brave leader Garibaldi is Dictator of 
Sicily. 



Ht = 2(10-6.5)=7.0. 



Date. 



Ha 

4 


H v 
5 


H w 


H d 


.5 








.5 








.5 








1.5 









.5 








.5 








-.5 








.5 








1 








.5 








.5 


1 






10.0 


6 


5.5 


10 



38 



Educational Guidance 



Name (Pupil No. 212). 



I. The completion of the Kingdom by capturing 
Rome (especially) and Venice; and making Emanuel's 
claim to the throne secure. 

II. Garibaldi, having been a sailor inherited their 
jovial demeanor and carriage. He was exceedingly 
adventurous, and, we hear of him in such countries 
as were engaged in war. He was tanned by exposure 
as a seaman, strong, muscular and athletic. He in- 
herited a trait of being able to rule and govern men 
as is shown by his checkered career. He was 
perpetually clad in a red shirt and sometimes a 
kerchief of the same brilliant hue, encircled his neck. 
His hair was luxurious and abundant which set off his 
appearance nicely. 

III. In April 1860 Garibaldi left Genoa in command 
of 1000 volunteers embarked on two Piedmontese 
vessels. He reach Marsala and marched his men 
landward to Palermo which he captured . Palermo 
had previously revolted and his campaign was in 
accordance to it. From Palermo he sailed to Calabria 
which he captured. He proceeded northwards and 
was joined by Emanuel. Together thay captured all 
of Italy except Rome and Venice. Garibaldi assumed 
the title of Dictator. Francis, King of the two Sicilies 
abdicated. Carassi was made secretary. Emanuel 
was proclaimed King and the first Parliament met 
1861, which represented all the individual states com- 
bined. (Deduct 1 for order of events) 



Date. 



Grading 

Ha Hy Hw Hd 



.5 
.5 
.5 

a 

-.5 

.5 

-.5 

.5 



1.5 



-1 



12 11.5 9 



Ht = 2(12-6.5) = 11. 



Special Tests and Their Significance 



39 



Name (Pupil No. 234). 



Date. 



I. The fall of Rome was probably the next impor- 
tant event, maybe Venice at the same time. 

II. Garibaldi was a strong man. As he had been in 
South America he was toughened to wild life. He was 
a man who was strong as a general and could com- 
mand troops well. 

He had black wavy hair and wore a red shirt. 

III. When Garibaldi left Genoa secretly he took 
with him a thousand men. These men were like 
King Arthur and his Knights of the Round' Table. 
When they came near Marsala two war vessels from 
Naples followed them but at the same time t wo English 
men-of-war were there and they delayed the men-of- 
war from Naples. Garibaldi reached Marsala and 
went to a telegraph office and was just too late to stop 
a message saying that they had arrived. He had the 
operator send the message that he mistook the vessels 
and that they were only merchant vessels. 



Ht=2(10.5-6.5)=8.0. 



Ha 


H v 


H w 


Hd 


4 


6 






.5 








.5 
.5 


1 






.5 








.5 








.5 








.5 








.5 








.5 








.5 








.5 








10.5 


7 


8 


3.5 



40 



Educational Guidance 



Name (Pupil No. 227). Date. 



Grading 



I. The two Sislies were united, no doubt. 

II. Garibaldi must have been stern and had good 
discipline to manage so many people, and train Italian 
soldiers. (He was perfectly honest as he said he 
would help Italy and did.) Garibaldi, was tall, 
had dark wavy hair that fell in waves over his 
crisp black eyebrows, his eyes stood out like black 
diamonds in a white velvet background. Garibaldi 
wore a flaring red shirt. 

III. Garibaldi left Genoa with a crew of a thousand 
men, sailed directly southward to Palermo ; when the 
people there heard that vessels had landed they sent a 
wireless of the news and also for help. Garibaldi 
arrived just in time to add a few words to the message. 
After he had conquored and captured Messina, and 
the other cities he worked his way north where 
another force joined him and together they captured 
Naples. 



Ht=2(-l-6.5) = -15. 



Ha 


Hy 


H w 


Ha 


4 


2 






{=1 

.5 








-1 








-1 








.5 








U 6 








.5 








.5 








-1 








.5 


-1 






-1 


1 


7.5 


8.5 



(Mj, Ej, Hj,) Interest Tests 

In attempting to test a pupil's interest in some given high 
school subject an error would likely be introduced if that subject 
alone were dealt with, as the pupil would readily see the object 
of the test and, possibly unconsciously, be influenced thereby. 
For purposes of tapping a pupil's personal preference it is very 
much more significant for him to say that of all vocations he 
prefers that of teaching mathematics, than for him to reply in 
the affirmative to the question "Would you rather teach mathe- 
matics for a vocation than to do anything else?" This illustra- 
tion serves to emphasize the difference in the nature of response 
of an individual when he is indicating a spontaneous preference 
from his response when he is accepting or rejecting a controlled 
choice. 

In order to insure such spontaneity and freedom of choice, an 
interest test was so devised as to cover impartially all the ordi- 



Special Tests and Their Significance 



41 



nary interests of a pupil. Because this test covers so broad a field 
it may be used equally well to measure a pupil's interest in lines 
other than mathematics, English and history, which are the 
lines for which its significance has been evaluated in this study. 
When graded along the line of English, the grade of this test is 
designated by E;, along the line of mathematics by Mi, and 
along the line of history by Hi. The grading of this test is 
accomplished by means of tables given on succeeding pages. 
Administration of test: The pupils were told to answer the ques- 
tions on the sheets handed them. As much time as was needed 
was given — most of the pupils finishing the task in 40 minutes. 



Interest Tests 

Name Date 

1. Go through the accompanying list of magazines and put an x opposite 
those with which you are not familiar, that is, opposite those of which you have 
never looked through at least two numbers. 

1. All Story 27. Hearst's 50. Pictorial Review 

2. American Boy 28. Home Needlework 51. Popular Mechan- 

3. American 29. Ill'd London News ics 

4. Argosy 30. L'illustration 52. Popular Science 

5. Atlantic Monthly 31. Illustrirte Zeitung Monthly 

6. Black Cat 32. Industrial Eng'g 53. Printer's Ink 

7. Blue Book 33. International Stu- 54. Puck 

8. Bookman dio 55. Red Book 

9. Cassier's 34. Ladies Home Jour- 56. Review of Reviews 

10. Century nal 57. St. Nicholas 

11. Colher's Weekly 35. LaFollette's 58. Saturday Evening 

12. Commoner 36. Leslie's Weekly Post 

13. Cosmopolitan 37. Life 59. Science 

14. Country Life in 38. Lippincott's 60. Scientific American 

America 39. Literary Digest 61. Scribner's 

15. Craftsman 40. McClure's 62. Smart Set 

16. Current Literature 41. Metropolitan 63. Strand 

17. Delineator 42. Modern Priscilla 64. System 

18. Electrical World 43. Moving Picture 65. Technical World 

19. Etude World 66. Theatre 

20. Everybody's 44. Munsey's 67. Woman's Home 

21. Good Housekeep- 45. Musician Companion 

ing 46. Natio'nal Geo- 68. Wilshire's 

22. Graphic graphic 69. World's Work 

23. Green Book 47. Outing 70. Youth's Compan- 

24. Hampton's 48. Outlook ion 

25. Harper's Weekly 49. Photographic 

26. Harper's Monthly Times 

Go through the list again, marking the five that interest you most A, B, C, 
D and E; A for the most interesting of all, B for the next most interesting, and 
so on. Do not spend much time in deciding exactly upon your preferences. 

2. Briefly tell why you particularly enjoy reading the magazine that you 
have marked A. 

3. Name three books which you have read in the last two years that have 

interested you very much. 1 

2 3 



42 



Educational Guidance 



4. Suppose that you have an hour's leisure time, in what outdoor amuse- 
ment would you prefer to spend it? 

5. Suppose that you have an hour's leisure time, in what indoor amusement 
would you prefer to spend it? 

6. Of the two amusements named in your answers to questions 4 and 5 
which do you prefer? 

7. If you had the opportunity, which one of the following would you attend, 
supposing each of them to be first class of its kind? Mark it A. 

1. Moving picture entertainment. 9. Boxing contest 

2. Circus 10. Band concert 

3. Football game 11. Political rally 

4. Baseball game 12. Light opera 

5. Track meet 13. Drama 

6. Musical comedy 14. Lecture, or stereopticon lecture, 

7. Vaudeville performance on a subject that interests you. 

8. Grand opera 

8. What occupation would you prefer as a life work? 

Which would you like next best? 

9. In the following list of words mark with a 3 those you know the meaning 
of perfectly and could define as a dictionary does. 

If you can explain in a general way the meaning of the word and would 
understand it when used in a sentence mark it with a 2. 

If you cannot explain its meaning but are vaguely familiar with it, mark it 
with a 1. 

If the word is entirely new to you and unknown, mark it with a 0. 

In doing this, go through the list four times, the first time marking the 3's, 
the second time the 2's, the third time the l's, and the last time the 0's. 

1. simile 32. physical valuation of railroads. 

2. primary election 33. score (in music) 

3. Mason and Dixon's line 34. commercial fertilizer 

4. creed 35. Magna Charta 

5. Acropolis 36. voucher 

6. rip saw 37. ohm 

7. hydrogen 38. string halt 

8. compound interest 39. fourth dimension 

9. cube root 40. piston rod 

10. paradox 41. Pythagorean proposition 

11. Saracens 42. single tax 

12. I. W. W. 43. stamen 

13. Whigs 44. hemstitch 

14. theosophy 45. Spanish Armada 

15. toga " 46. statute of limitations 

16. block plane 47. coherer 

17. NaCl 48. vertebrate 

18. fissure 49. parallelogram 

19. equation 50. omelette 

20. guillotine 51. Reichstag 

21. prose 52. Commerce Court 

22. syndicalism 53. states' rights 

23. H 2 54. space bar 

24. transubstantiation 55. giblets 

25. gladiator 56. Australian ballot 

26. debit 57. mollusk 

27. gravity cell 58. perspective 

28. strata 59. fireless cooker 

29. improper fraction 60. mortgagee 

30. lever 61. referendum 

31. ragtime 62. Formosa 



Special Tests and Their Significance 43 

10. Tell what each of the following words means as well as you can. 

a. simile 

b. cube root 

c. improper fraction 

d. ragtime 

e. physical valuation of railroads 

f . commercial f ertilizer 

g. ohm 

h. Pythagorean proposition 

i. single tax 

j . hemstitch 

k. vertebrate 

1. parallelogram 

m. omelette 

The last two questions are not solely for the purpose of testing 
the pupil's interest, as they test his range of information as well. 
They constitute a vocabulary test in which the words were chosen 
because of their specific bearing upon all the usual high school 
courses and in addition upon religion and politics, in order to 
cover the intellectual field. 

Anyone who has read the answers of a few pupils to the ques- 
tions in this test must feel that strong individual differences are 
shown. There is much to indicate that the data are highly signifi- 
cant as evidence of interest, but the problem of expressing this 
in numerical terms and with reference to specific high school 
courses is far more elusive than simply the determination that 
the data are significant. For purposes of evaluation, it would be 
possible, theoretically, to have a large number of judges grade 
each pupil's paper upon the various questions with reference to 
the significance of each of the questions in turn as evidence of 
interest, severally, in mathematics, English and history. Prac- 
tically this method is valueless, as judges with sufficient leisure 
and patience could not be found and because their work would 
apply only to the actual papers graded and would be of no aid to 
another party desiring to give the test. A result embodying all 
the advantages of the former method and none of its disadvan- 
tages, can be obtained by having a sufficient number of judges 
grade the questions for all the probable answers. With a table 
of such gradings for each question, it is then only a matter of a 
single grader comparing the answers of the pupils with the grad- 
ings of the tables. Anyone is then able to give and grade the 
test with an accuracy which is very nearly as great as the accu- 
racy of the original grading of the expert judges. This second 



44 



Educational Guidance 



method, which has been used, will be clearer when illustrated by 
reference to the specific questions. 



Grading of the Interest Tests 

Questions 1 and 2 — Magazines. 

Each of the magazines listed was graded from zero to ten for its significance 
as evidence of interest and information along the line of English and again 
with reference to history, by four judges (except that only three graded fifteen 
of the least familiar magazines), three of whom are psychologists and familiar 
with grading of this nature, and the fourth a librarian. The average, to the 
nearest integer, of the grades of the different judges is the grade given for each 
magazine in the following table: 



Grade 



Grade 



Eng. 


Hist 


1 





2 


1 


5 


5 


1 





10 


4 


1 











8 


2 


2 


1 


7 


4 


4 


7 


6 


9 


4 


2 


5 


1 


5 


1 


9 


4 


3 





3 


1 


3 


2 


5 


5 


4 


2 


4 


7 








4 


5 


4 


6 


6 


3 


4 


5 


3 





4 


7 


4 


7 


4 


7 


3 


2 


3 


2 


4 


1 


5 


9 


4 


7 



1. All Story 

2. American Boy 

3. American 

4. Argosy 

5. Atlantic Monthly 

6. Black Cat 

7. Blue Book 

8. Bookman 

9. Cassier's 

10. Century 

11. Colher's Weekly 

12. Commoner 

13. Cosmopolitan 

14. Country Life in 

America 

15. Craftsman 

16. Current Literature 

17. Delineator 

18. Electrical World 

19. Etude 

20. Everybody's 

21. Good Housekeeping 

22. Graphic 

23. Green Book 

24. Hampton's 

25. Harper's Weekly 

26. Harper's Monthly 

27. Hearst's 

28. Home Needlework 

29. Ill'd London News 

30. L'illustration 

31. Illustrirte Zeitung 

32. Industrial Eng'g 

33. International Studio 

34. Ladies' Home Journal 

35. LaFollette's 

36. Leslie's Weekly 



Eng. 
3 
5 
7 
5 
1 
3 
1 

1 
3 
5 
3 
7 
3 
2 
2 
2 

1 

2 

5 
6 
4 
3 
3 
7 
3 
2 
2 
2 
1 
4 

3 
5 
5 



Hist. 
1 

2 
7 
4 




1 

2 
9 
1 
8 
2 

1 
1 



1 



8 
1 
4 
2 
3 
3 


1 
1 

1 



37. Life 

38. Lippincott's 

39. Literary Digest 

40. McClure's 

41. Metropolitan 

42. Modern Priscilla 

43. Moving Picture 
World 

44. Munsey's 

45. Musician 

46. National Geographic 

47. Outing 

48. Outlook 

49. Photographic Times 

50. Pictorial Review 

51. Popular Mechanics 

52. PopularScience 
Monthly 

53. Printer's Ink 

54. Puck 

55. Red Book 

56. Review of Reviews 

57. St. Nicholas 

58. Saturday Ev'g Post 

59. Science 

60. Scientific American 

61. Scribner's 

62. Smart Set 

63. Strand 

64. System 

65. Technical World 

66. Theatre 

67. Woman'sHomeCom- 
panion 

68. Wilshire's 

69. World's Work 

70. Youth's Companion 



Special Tests and Their Significance 45 

The correlations between the grades given by judges 1, 2, 3 and 4 are as 
follows : 




Average . 863 

Taking the number of judges for each magazine as three and one-half, the 
reliability coefficient equals .956. 

The single grade given for these questions is the average grade for the 
magazines after altering the grade of the magazine marked "A" (usually about 
If points) upon the basis of the answer to question 2, and weighting maga- 
zines A, B, C, D, and E 10, 8, 6, 4, and 2 respectively. The sample grading 
of the entire test, given on page 56, will show the steps in detail. 

The reliability coefficient for the grading of each magazine is .956, but the 
reliability of the average of a number of such grades is higher. A factor tend- 
ing in the other direction is the method of grading the magazine marked "A. " 
The alteration of the grade of this magazine is not arbitrary, but left to the 
grader, and therefore its reliability is somewhat less than that of the maga- 
zines that have been graded by three or four judges. The net result of these 
two factors is probably to make the reliability of the grade given for the 
question about the same as the reliability of the grading of the magazines by 
the judges. 

Question 3 — Books. 

The establishment of a guide for the grading of question 3 offers greater 
difficulties than was the case with question 1, for the reason that the number 
of books which may be preferred is unlimited. However, quite a number of 
books were repeatedly chosen, so that a grading for books for English and 
history covering 300 or so of the most frequent choices does cover a very large 
per cent of the books chosen. Furthermore, as each pupil chooses three books, 
it is much more than likely that two of the three will be books that are graded, 
or books by the same author as graded books, so that the grading actually is 
quite objective. The following is such a list, and the grades given, expressed 
as deviations from the mean, are the averages of the grades of from two to four 
judges, about one-half being graded by three or more judges. This list of 
about 300 titles is part of a larger list which included all the books preferred 
by the pupils. The larger fist was given to four judges — two librarians and 
two others familiar with such work. The directions to the judges were to grade 
the books for English and history according to the following scheme: 

Grade English History 

1 The best literature. Straight histories. 

2 Excellent. Books that are mainly historical. 

Historical biographies, etc. 

3 Good. Partly historical. Historical fiction. 

4 Medium. Fiction or adventure with traces of 

historical material. 

5 Poor. Adventure, etc., with no claim to any 

historical matter, but with lively 
action and plot. 

6 Very poor — semi-trashy. Non-historical fiction. 

7 Pure trash. Books with neither plot nor historical 

background, e. g., Electricity for 
Beginners. 



46 



Educational Guidance 



The average correlation between the gradings of two judges is .882 for the 
English grading, and .720 for the history grading. The reliability coefficient, 
calling the number of judges 2\ , is, for the English grading .947, and for the 
history grading .861. Since all the books chosen are not in the following list, 
and since certain of those not so listed can be graded if the grader is familiar 
with the book or with the author, the reliability of the resulting grade of each 
book is somewhat less than the reliability coefficient just given. 

The gradings from 1 to 7 of the different judges were combined into single 
grades, expressed as deviations from the mean, 1 and this is the grade given in 
the following table: 



Author 

Scott 

Eliot 

Clemens 

Doyle 

Roosevelt 

Maeterlinck 

Irving 

Montgomery 

<< 

Locke 

F. H. Smith 

Franklin 

Stanley 

Haggard 

Wallace 

M. Warde 

McCutcheon 

Thompson-Seton 

Wiggin 

Stevenson 

Vance 

White 

Dickens 

Farnol 

London 
Kipling 
Stockton 

Garland 
Dumas 

it 

Dickens 
Churchill 
L. Scott 

Dumas 

it 

Gaskell 
Barbour 

Churchill 

it 

Trowbridge 

Rostand 

1 See Appx. p. 101. 



Title 

Abbot 

Adam Bede 

Adventures of Tom Sawyer 

Adventures of Sherlock Holmes 

African Hunt 

Aglavine and Lysette 

Alhambra 

Ann of Avonlea 

Ann of Green Gables 

Aristide Pujol 

Armchair at the Inn 

Autobiography of Benjamin Franklin 

Autobiography of Henry M. Stanley 

Ayesha 

Ben Hur 
Betty Books 
Beverly of Graustark 
Biography of a Grizzly 
Birds' Christmas Carol 
Black Arrow 
Black Bag 
Blazed Trail 
Bleak House 
Broad Highway 

Call of the Wild 

Captains Courageous 

Casting Away of Mrs. Leeks and Mrs. 

Aleshine 
Cavanaugh, Forest Ranger 
Chevalier de Maison Rouge 
Chicot the Jester 
Christmas Carol 
Coniston 

Counsel for the Defense 
Count of Monte Cristo 
Countess de Charny 
Cranford 
Crimson Sweater 
Crisis 
Crossing 
Cudjo's Cave 
Cyrano de Bergerac 



Grade 



Eng. 


Hist, 


1.2 


1.2 


2.0 


-.2 


.2 


.0 


.2 


.0 


• .2 


.0 


.9 


- .8 


1.4 


2.2 


.4 


- .8 


.4 


- .8 


■ .2 


- .8 


.2 


- .8 


.2 


1,5 


.2 


1.5 


1.2 


- .8 


.5 


1.2 


• .8 


- .8 


1.7 


- .4 


■ .2 


- .4 


.1 


- .8 


.8 


- .6 


1.5 


- .8 


.2 


.9 


1.2 


- .2 


.6 


- .4 


.4 


.5 


.4 


- .4 


.0 


- .8 


.6 


.4 


.5 


1.2 


.5 


.2 


1.3 


— .8 


.1 


.6 


.3 


- .8 


.5 


.8 


.5 


1.2 


.1 


- .6 


.8 


- .8 


.1 


1.2 


.1 


1.2 


1.7 


- .4 


1.4 


.9 



Special Tests and Their Significance 



47 



Author 



Title 



Grade 







Eng. 


Hist 


Eliot 


Daniel Deronda 


1.4 


.5 


Stevenson 


David Balfour 


.8 


.5 


Dickens 


David Copperfield 


1.1 


- .4 


Ferber 


Dawn O'Hara 


- .6 


- .7 


Aguilar 


Days of Bruce 


- .3 


1.1 


Cervantes 


Don Quixote 


1.2 


.9 


Dickens 


Dombey and Son 


1.1 


- .4 


Major 


Dorothy Vernon of Haddon Hall 


- .6 


.7 


Bacheller 


Dri and I 


.1 


.9 


n 


Eben Holden 


- .2 


- .5 


Alcott 


Eight Cousins 


- .2 


- .8 


Tennyson 


Enoch Arden 


1.3 


- .8 


Longfellow 


Evangeline 


.4 


.9 


Drummond 


Evolution of Man 


.2 


.4 


Spenser 


Faerie Queene 


2.1 


- .8 


Poe 


Fall of the House of Usher 


1.2 


- .8 


Gaboriau 


File Number 113 


.1 


.0 


Fothergill 


First Violin 


- .4 


- .8 


Chaplin 


Five Hundred Dollars 


-1.5 


- .9 


Porter 


Freckles 


- .4 


- .8 


Read 


Foul Play 


.2 


.0 


Poe 


Gold Bug 


1.2 


- .8 


McCutcheon 


Graustark 


-1.7 


- .5 


Dickens 


Great Expectations 


1.1 


- .5 


Holmes 


Gretchen 


-2.7 


- .8 


Shakespere 


Hamlet 


2.3 


.4 


Dodge 


Hans Brincker 


- .8 


- .5 


Porter 


Harvester 


.1 


.2 


Thackeray 


Henry Esmond 


1.4 


.9 


Shakespere 


Henry V 


2.3 


.9 


Kelly 


Her Little Young Ladyship 


- .4 


- .8 


Redpath 


History of America 


.4 


3.5 




Hollow of Her Hand 


-1.4 


- .9 


Leblau 


Hollow Needle 


- .2 


.0 


Ford 


Honorable Peter Sterling 


- .4 


- .2 


Mulford 


Hopalong Cassidy 


- .9 


- .8 


Doyle 


Hound of the Baskervilles 


- .2 


.0 


Hawthorne 


House of Seven Gables 


1.2 


- .8 


Rohlfs 


House of the Whispering Pines 


-1.2 


.0 


Clemens 


Huckleberry Finn 


.2 


- .5 


Clemens 


Innocents Abroad 


.2 


- .8 


Davis 


In the Fog 


- .4 


.1 


Crawford 


In the Palace of the King 


- .2 


.7 


Deland 


Iron Woman 


- .4 


- .8 


Scott 


Ivanhoe 


1.2 


1.2 


McCutcheon 


Jane Cable 


-1.7 


- .8 


Bronte 


Jane Eyre 


.8 


- .8 


Ford 


Janice Meredith 


- .4 


1.2 


Craik 


John Halifax, Gentleman 


.2 


- .8 


Kipling 


Jungle Book 


.4 


- .8 



48 



Educational Guidance 



Author 



Title 



Grade 







Eng. Hist 


Scott 


Kenilworth 


1.2 1 


2 


Smith 


Kennedy Square 


- .4 - 


8 


Stevenson 


Kidnapped 


.8 


5 


Kipling 


Kim 


.4 - 


5 


Irving 


Knickerbocker History of New York 


.8 


8 


Williamson 


Lady Betty Across the Water 


-1.4 


8 


Scott 


Lady of the Lake 


1.2 


5 


Cummins 


Lamplighter 


- .9 


5 


Lytton 


Last Days of Pompeii 


.8 1 


2 


Cooper 


Last of the Mohicans 


.4 


9 


Reed 


Lavender and Old Lace 


-1.7 


8 




Letters of Abraham Lincoln 


.5 2 


2 


Johnston 


Little Colonel in Arizona 


- .9 - 


8 


it 


Little Colonel at Boarding School 


- .9 - 


8 


Kipling 


Light that Failed 


.2 - 


8 


Dickens 


Little Dorrit 


1.1 - 


4 


Alcott 


Little Men 


.1 - 


8 


Barrie 


Little Minister 


.6 


8 


Fox 


Little Shepherd of Kingdom Come 


- .4 - 


2 


Alcott 


Little Women 


.1 - 


8 


Blackmore 


Lorna Doone 


.2 


9 


Parrish 


Love under Fire 


— .8 


2 


Rice 


Lovey Mary 


- .6 - 


8 


Austen 


Mansfield Park 


.5 


8 


Rinehart 


Man in Lower Ten 


-1.0 


5 


London 


Martin Eden 


.5 


8 


Dickens 


Martin Chuzzlewit 


1.1 


2 


Bosher 


Mary Cary 


- .8 


8 


Zangwill 


Master 


.2 - 


8 


Corelli 


Master Christian 


-1.2 


8 


Eliot 


Mill on the Floss 


1.4 - 


8 


Marryat 


Mr. Midshipman Easy 


-1.2 


8 


Hugo 


Miserables, Les 


1.3 1 


2 


Lincoln 


Mr. Pratt 


-1.2 


8 


Barclay 


Mistress of Shenstone 


- .7 


8 


Rice 


Mrs. Wiggs of the Cabbage Patch 


- .6 


8 


Abbott 


Molly Make-believe 


- .6 - 


8 


Collins 


Moonstone 


- .2 - 


8 


Norris 


Mother 


- .4 - 


8 




Mother Carey's Chickens 


- .4 


8 


Spearman 


Mountain Divide 


- .8 


6 


Shakespere 


Much Ado About Nothing 


2.3 


8 


Verne 


Mysterious Island 


-1.2 - 


4 


Beach 


Ne'er Do Well 


- .9 


4 


it 


Net 


-1.2 - 


8 


Thackeray 


Newcomes 


1.4 - 


6 


Dickens 


Nicholas Nickleby 


1.1 


2 


Hugo 


Notre Dame 


1.3 


5 


Homer 


Odyssey 


2.3 


9 


Dickens 


Old Curiosity Shop 


1.1 


4 


Page 


Old Gentleman of the Black Stock 


- .2 - 


8 


Dickens 


Oliver Twist 


1.1 - 


4 


Burnham 


Open Shutters 


- .8 


8 



Special Tests and Their Significance 



49 



Author 


Title 


Grade 








Eng. 


Hist. 


Darwin 


Origin of Species 


- .6 


- .4 


Alcott 


Our Helen 


.2 


— . 


8 


Dickens 


Our Mutual Friend 


1.1 


— . 


4 


E. Smith 


Palace Beautiful 


-1.2 


— 


8 


Cooper 


Pathfinder 


.2 




7 


Wells 


Patty's College Days 


-1.2 


— . 


8 




Personal Memoirs of U. S. Grant 


- .4 


2. 


6 


Dickens 


Pickwick Papers 


1.1 


— . 


1 


Cooper 


Pioneers 


- .2 




3 


Flammarion 


Popular Astronomy 


- .9 


-1 


4 


Austen 


Pride and Prejudice 


.4 


— . 


8 


Clemens 


Prince and the Pauper 


.2 


— 


8 


Johnson 


Prodigious Hickey 


-1.2 


— 


8 


Aldrich 


Prudence Palfrey 


.1 


— 


5 


Harrison 


Queed 


.1 


— 


4 


Scott 


Quentin Durward 


1.1 


1 


2 


Sienkiewics 


Quo Vadis 


.4 


1 


2 


Hornung 


Raffles 


-1.7 


— 


4 


Jackson 


Ramona 


.4 




5 


Wiggin 


Rebecca of Sunnybrook Farm 


- .2 


— 


8 


Lytton 


Rienzi 


.8 


1 


2 


Parkman 


Robin Hood 


- .8 




5 


Thompson-Seton 


Rolf in the Woods 


- .2 


— 


4 


Le Gallienne 


Romance of Zion Chapel 


.1 


— 


8 


EUot 


Romola 


1.9 




9 


Barclay 


Rosary 


-1.2 


— 


8 


Alcott 


Rose in Bloom 


.1 


— 


8 


Hope 


Rupert of Hentzau 


-1.0 


— 


4 


Hawthorne 


Scarlet Letter 


1.1 




3 


Porter 


Scottish Chiefs 


- .4 


-1 


2 


London 


Sea Wolf 


.5 


— 


4 


Kipling 


Seven Seas 


.5 


— 


S 


Haggard 


She 


-1.4 


— 


4 


Wright 


Shepherd of the Hills 


.1 


— 


8 


Goldsmith 


She Stoops to Conquer 


1.1 


— 


4 


EUot 


Silas Marner 


1.9 


— 


2 


Porter 


Song of the Cardinal 


.1 


— 


8 


London 


Son of the Sun 


.5 


— 


8 


Barr 


Souls of Passage 


- .9 


— 


8 


Reed 


Spinner in the Sun 


-2.2 


— 


8 


Cooper 


Spy 


.4 


1 


2 


Schreiner 


Story of an African Farm 


- .4 


— 


.2 


Keller 


Story of My Life 


- .2 


— 


.8 


Johnson 


Stover at Yale 


- .9 


— 


8 


King 


Street Called Straight 


-1.0 


— 


8 


Vaile 


Sue Orcutt 


- .8 


— 


.6 


Wyss 


Swiss Family Robinson 


- .7 


— 


.2 


Dumas 


Taking the Bastile 


.5 


1 


.2 


Dickens 


Tale of Two Cities 


1.1 


1 


.2 


Scott 


Talisman 


1.1 


1 


.2 


Jacobs 


Texas Blue Bonnet 


-1.0 


— 


.8 


Porter 


Thaddeus of Warsaw 


- .3 




.8 



50 



Educational Guidance 



Authob 



Title 



Grade 







Eng. 


Hist 




Thoughts of Marcus Aurelius 


.7 


- .1 


Dumas 


Three Guardsmen 


.5 


1.2 


Jerome 


Three Men in a Boat 


- .4 


- .8 


Glyn 


Three Weeks 


-2.3 


- .8 


McCutcheon 


Truxton King 


-1.7 


- .8 


Verne 


Twenty Thousand Leagues under the 








Sea 


-1.2 


- .8 


Stowe 


Uncle Tom's Cabin 


- .2 


.9 


Ouida 


Under Two Flags 


- .4 


.5 


Henty 


Under Drake's Flag 


-2.4 


.9 


Alcott 


Under the Lilacs 


.1 


- .8 


Thackeray 


Vanity Fair 


1.4 


- .2 


Goldsmith 


Vicar of Wakefield 


1.1 


- .8 


Wister 


Virginian 


- .2 


- .8 


Scott 


Waverley 


1.1 


1.2 


Reed 


Weaver of Dreams 


-1.7 


- .8 


Malone 


West Point Yearling 


- .6 


- .8 


Doyle 


White Company 


- .2 


.3 


London 


White Fang 


.4 


- .8 


Thompson-Seton 


Wild Animals I Have Known 


- .2 


- .4 


King 


Wild Olive 


- .8 


- .8 


Scott 


Woodstock 


1.1 


1.2 


Rohlfs 


Woman in the Alcove 


-1.6 


.0 


Hawthorne 


Wonder Book 


1.1 


- .8 


Alger 


Young Adventurer 


-2.2 


- .8 


Bennett 


Your United States 


- .2 


.3 



The grade for question 3 is the average grade for the three books, weighting 
the first, second and third choices 3, 2, and 1 respectively. 

Since this grade is an average of three grades, its reliability is greater than 
that of a single book, and is probably close to .94 for English and .86 for history. 

Questions 4, 5 and 6 — Sports. 

The same general method used in establishing a guide for the grading of 
books, has here been used in drawing up a guide for the grading of sports, 
except that the grades were not expressed as deviations from a mean. The 
grading was on a basis of zero to ten, and the judges consisted of three per- 
sons experienced in such grading. The average correlation between the grad- 
ings of the different judges, when English and history are combined into a 
single correlation table, is .239. The reliability coefficient for the grading 
is, therefore, .485. The grading is separate for the preferences of boys and 
girls, as shown in the following table: 



Special Tests and Their Significance 



51 



Sports 



Motoring 

Baseball 

Basketball 

Bicycling 

Cards 

Domestic activities (cooking, sewing, etc.) 

Drawing, painting 

Fishing 

Football 

Hockey 

Horseback riding 

Pool or billiards 

Musical practice 

Reading 

Rowing or sailing 

Shop work 

Skating 

Swimming 

Tennis 

Theatre 

Running games 

Walking 

Watching a game 



E 
3 

1 
1 
1 

1 



Boys 
I H 
3 

1 
1 
1 
1 



M 
2 

2 

2 



Girls 




E 


H 


M 


3 


3 


2 


1 


1 


2 


1 


1 


2 


1 


1 


2 


3 


2 


1 


3 


4 


3 


1 


1 


1 


1 


1 


2 


2 


2 


1 








2 


2 


2 


2 


9 


9 


2 


1 


1 


3 


1 


1 


3 


1 


1 


1 


1 


1 


1 


5 


5 





1 


1 


1 


1 2 


2 


| 1 



The grade for the question is the average, counting the indoor choice once, 
the outdoor choice once and the preference once. Since this grade is an 
average of three, one of them, however, a repetition, there is a slight tendency to 
increase the reliability of the grading over that of each sport singly. This 
tendency is probably counterbalanced by the fact that all possible sports are 
not included in the above list, and the grader must at times use his judgment 
in the matter. In view of these two facts, it is likely that the reliability of 
the grading is about .48. 

Question 7 — Entertainments. 

The general method used in establishing a guide for the grading of magazines 
was followed here. Grading was upon the basis of zero to ten, and the judges 
consisted of four persons experienced in such work. The average correlation 
between the gradings of the judges, combining English and history into a 
single correlation table, is .929, so that the reliability coefficient of the grading is 
equal to .981. The grading follows: 



Entertainments 



Moving pictures . 
Circus 



Football game 

Baseball game 

Track meet 

Musical comedy 

Vaudeville 

Grand opera 

Boxing contest 

Band concert 

Political rally 

Light opera 

Drama 

Lecture, or stereopticon lecture on a subject that interests you. . 

The grade given for the question is the grade of the entertainment marked 
'A," so that the reliability coefficient of this grade is .981. 



E H 



3 


4 


























1 











7 


4 








2 


1 


4 


10 


3 





9 


7 


9 


7 



52 



Educational Guidance 



Question 8 — Vocations. 

Here again, the number of choices is unlimited, so that the method used in 
the grading of sports is the one followed. The following list of vocations was 
drawn up after examination of all the choices of the pupils, and was graded by 
four judges. The average correlation between the gradings of the different 
judges, the mathematics, English and history gradings being combined into 
a single table, is .693, so that the reliability coefficient of the grading is .901. 



Vocations 



Actor 

Artist 

Athlete, professional 

Author 

Banker 

Broker 

Business 

Carpenter 

Decorator or designer 

Doctor 

Journalist 

Engineering 

Architectural 

Electrical 

Civil 

Marine 

Mechanical 

Mining 

Structural 

Farming 

Forestry 

Housekeeper 

Lawyer 

Lecturer 

Librarian 

Milliner 

Musician 

Member of navy 

Nurse 

Politician 

Secretary 

Singer 

Charity worker 

Dressmaker 

Teacher 

Domestic science 

English 

Kindergarten 

Physical training or dancing . 



E 

8 
6 

10 
6 
5 
4 
2 



Boys 

H 

5 

6 
1 

7 
5 
4 

4 

2 



M 
1 
1 

2 
8 
6 
6 
5 



3 

2 
9 
8 
9 
9 
9 
10 
9 
9 
2 
2 



E 
7 
6 



Girls 
H 

4 
6 



4 
6 
3 

8 

6 

10 



M 


1 



Question 9 — Vocabulary. 

The grading of the words followed the general scheme used in grading the 
magazines. A number of words are graded zero by all the judges for their sig- 
nificance in one or all of the three lines, and as these do not enter into the 
grade which the pupil received, they have been omitted in calculating the 
reliability of the grading for mathematics, English and history, though simply 
as a measure of the reliability of the grading this is not desirable. The inclu- 
sion of these zero gradings would increase the reliability coefficient. The 
reliability differs considerably for English from that for mathematics and 



Special Tests and Their Significance 53 

history so that the coefficients are calculated separately. The average cor- 
relation for the different judges, excluding the zeros, as stated, between the 
gradings of the words, equals for mathematics .785; for English .542; for his- 
tory .795, and the average for all is .707. Since three judges graded all the 
words, the reliability coefficients for the grades of these subjects are .916 for 
mathematics, .780 for English and .921 for history; an average of .872. 

The grade the pupil receives for mathematics is the sum of the various 
words checked, after it has been multiplied by the factor of accuracy obtained 
in the last question; and similarly for English and history. Since this grade 
is made up of a considerable number of grades, whose reliability is given above, 
the reliability of the grade, before multiplication by the factor of accuracy, 
is appreciably greater than the reliability of the grading of each of the words, 
and is probably not less than .96 for mathematics and history, and not less than 
.92 for English. 

As given in the next section, the reliability of the factor of accuracy is 
about .95, so that the reliability of the grade for the question is close to .91 
for mathematics and history and in the neighborhood of .87 for English. 

Question 10 — Factor of Accuracy. 

To determine the accuracy of the pupil's estimate of his knowledge, he is 
asked to define 13 of the words upon which he has previously expressed a judg- 
ment as to his familiarity with them. His definitions of these 13 words are 
graded 1, 2, 3, or 4. The sum of these grades gives a quantitative statement 
of the extent of the pupil's knowledge of the 13 words. This sum, which may 
be called the measure of the pupil's actual knowledge, divided by his claim, 
gives the factor of accuracy sought. In adding up the marks which constitute 
the pupil's own claim, it will be noticed that not infrequently the pupil has 
erased or marked over his previous marking, giving himself a lower mark in the 
second case. In all such cases the first grade put down by the pupil is the grade 
used. A magnifying glass may be of assistance, though it is seldom needed, 
the pupil making the correction probably not because he wishes to be dis- 
honest, but because he realizes that he has over-estimated his knowledge and 
wishes to be honest and straighten it out. 

The reliability of this factor of accuracy is undoubtedly high, and is esti- 
mated at .95. 

Two Kinds of Reliability Coefficients 

The reliability coefficients given, mean simply that the gradings of the 
questions as determined by the grader with the help of the tables formulated 
by the various judges, would probably correlate with the gradings determined 
by a second grader with the help of tables drawn up by a second set of judges, 
to the extent indicated. They do not mean that the gradings of the prefer- 
ences of the pupils would correlate with similar gradings derived from different 
but similar data, to the extent indicated. The extent of this latter correla- 
tion can be determined for those questions that are not exhaustive, i. e., those 
for which a second similar test is possible. The vocabulary and the factor 
of accuracy questions fulfill these conditions. For the vocabulary test it 
would only be necessary to devise a second list of words, as similar as possible 
to the words in this list, have their significance evaluated by the same number 
of qualified judges as here used and have a second person grade them, using 
the guides of the judges. The correlation between the grades of the pupils in 
this second vocabulary test and their grades in the test here given, gives the 
reliability coefficient of the grading as a measure of the trait in question, based 
upon such a limited sampling as that here used. 

Another method is to treat the halves of the present test as separate vocab- 
ulary tests and calculate the correlation between them. This latter method 
has been used for the history grading, giving a correlation of .620, derived 
from a sample of 36 pupils. The English and mathematics data are not so 



54 Educational Guidance 

extensive, so that the correlation in those cases would be somewhat smaller. 
Since the correlation between the gradings of the halves of the history words 
equals .620, the extent to which the two halves combined, or the whole test, 

TIT 

would correlate with a similar test, is given by the usual formula ; — • 

l + (n — l)r 
This value equals .765, which is the reliability coefficient of the data as a 
measure of the pupil's vocabulary of historical words (this is, of course, before 
multiplication by the factor of accuracy). 

Dividing the words used in determining the factor of accuracy, into two 
parts, one part consisting of words a, b, c, d, e, m and the other part of the 
balance, and proceeding in a similar manner, it is found that the reliability of 
the obtained factor of accuracy equals .453. The smallness of this reliability 
coefficient shows the limitation of the vocabulary test used, while the fact that 
the present test is significant, as will be shown later, demonstrates that a more 
accurate determination of the factor of accuracy would result in a vocabulary 

TIT 

test of greater and very substantial value. Using the formula — — — 

l + (w — l)r 

the reliability of a test, based upon any given number of words, may be ob- 
tained, and for certain numbers it is as follows : 

Question similar to No. 9, except In which case the coefficient of 

that number of words .= reliability = 

124 .867 

186 .907 

76 .80 

Question similar to No. 10, except 
that number of words = 

26 .624 

39 .713 

52 .768 

24 .60 

37 .70 

63 .80 

It is apparent from these data that the determination of the factor of accu- 
racy should be based upon about three times as many words as have been 
used, to make its reliability about the same as the grading of the history 
words. 



Special Tests and Their Significance 55 

Grade for Entire Interest Test 

Mathematics : 

The combination of the mathematics grades for the various 
questions into a single grade for the test, designated as M-„ is 
as follows : 

M i = 2(.2M Spt8 +.05M Ent8 +.4M V oc 8 +1.0F of A + .08M Wds ). 

The factor 2 is introduced to secure a better distribution. 
Mspt 8 = grade of the sports for their mathematical significance, 
and similarly for other designations. 1 

English : 

The single grade of the test for English is as follows : 

E i = .2E Spt8 +.05E Ents +.4Evoc8-5.0FofA+.08E wd8 +3.3E Mw 
+.165E Bks . 

History : 

The single grade of the test for history is as follows : 

H i = .2H Spt8 +.05H En t s +.4Hvoc S -2.0F of A+.08H wd8 +3.3H Mag a 
+ .165HBk 8 - 

Sample grading of the interest test: 

The occasions for the exercise of judgment in this test are so few that a very 
few illustrations will suffice to make the method clear. To avoid decimals in 
the samples that follow, 5 times the measures contributing to Mi and 10 times 
those contributing to Ei and Hi are calculated. 



1 See Appx., pp. 101-103. 



56 



Educational Guidance 



Name (Pupil No. 90). 



Magazines Checked in Question I 



Date. 



(4) 



(6) 



X American 

X Atlantic Monthly 

X Blue Book 

X Bookman 

D Century 

X Collier's Weekly '.'.' 

X Cosmopolitan 

X Country Life in America 

C Craftsman 

X Current Literature 

X Delineator 

X Electrical World 

X Etude 

X Everybody's 

X Good Housekeeping 

X Green Book 

X Hampton's 

X Harper's Weekly 

X Harper's Monthly 

X L'illustration 

X International Studio 

X Ladies' Home Journal 

X Leslie's Weekly 

XLife 

X Lippincott's 

X Literary Digest 

X McClure's 

X Metropolitan 

X Modern Priscilla 

X Munsey's 

A National Geographic (lb) 

(See question 2) 

X Outing 

X Pictorial Review 

E Popular Mechanics (2) 

X Popular Science Monthly 

X Puck 

X Red Book '.....'. 

X Review of Reviews 

B St. Nicholas (8) 

X Saturday Evening Post 

X Science 

X Scientific American 

X Scribner's 

X Smart Set 

X Strand 

X Technical World 

X Woman's Home Companion 

X World's Work 

X Youth's Companion 

X Outlook 



Geade of 
Same for 



M 



Frequency (75) 

Average grade 

33 times average grade 



E 
5 

10 

8 
28 
4 
4 
5 
30 
9 
3 
3 
3 
5 
4 

4 
4 
6 
4 
3 
4 
4 
3 
5 
7 
5 
1 
3 
1 
50 

3 

2 
4 
2 
2 

5 
48 
4 
3 
3 
7 
3 
2 
2 
4 
5 
5 
7 



336 
4.5 



H 
5 
4 

2 
16 
7 
2 
1 
6 
4 

1 
2 
5 
2 

5 
6 
3 
7 
2 
1 
7 
1 
2 
7 
4 


1 
90 

1 

2 
1 
1 

8 
8 
4 
2 
3 
3 


1 
1 
8 
2 
8 



246 
3.3 



Factor Con- 
tributing 
to Total 
Grade 



Mi 



Ei 



Hi 



149 



109 



Special Tests and Their Significance 



57 



Answer to question 2 : 

"The National Geographic Magazine is interesting because 
it tells so many interesting things of people we know very 
little, and of places none of us have seen/' 

No warrant is found in tliis answer for altering the grade 
assigned to the National Geographic Magazine. 
Answer to question 3 : 

1. Spenser's — Faerie Queene (3) 6.3 -2.4 

2. Scott's— The Abbot (2) 2.4 2.4 

3. Poe's— Fall of the House of Usher (1) 1.2 



Frequency . . . 
Average grade . 



(6) 



1.65 times average grade 

Answer to question 4 : 

"In a long walk through the woods.". 
Answer to question 5: 

"Reading." 

Answer to question 6 : 

"Number 4" 



Frequency (3) 

Average grade 

2 times average grade 

Answer to question 7 : 

"A" Grand Opera 

.5 times the grade 

Answer to question 8: 

1st choice: "Landscape Architect (2) 

2d " "Designing." 



Frequency 

Average grade 

4 times average grade . 



(3) 



4 
1.3 



19 
6.3 



9.9 
1.67 



11 
3.7 



14 

4.7 



-.13 

1 
9 
1 



11 

3.7 



17 
5.7 



25 



19 



23 



Answer to question 9 : 
Pupil's 
mark 



Word 



simile 

primary election 

Mason and Dixon's line . 

creed 

Acropolis 

rip saw 

hydrogen 

compound interest 

cube root 

paradox 

Saracens 

I. W. W 

Whigs 

theosophy 

toga 

block plane 

NaCl 

fissure 





15 








27 






6 


6 






9 


27 






6 


30 
6 






6 


27 






9 


3 






6 


27 
3 







58 



Educational Guidance 



Pupil's 
mark 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

1 

3 

3 

2 

3 

3 

3 

3 



3 

3 

3 



3 

3 

3 

3 

3 

3 

3 

3 

3 



3 

3 

2 

3 



2 

3 

3 

3 

3 
3 



Word 



equation 

guillotine 

prose 

syndicalism 

h 2 o ;.; 

transubstantiation 

gladiator 

debit ' 

gravity cell 

strata 

improper fraction 

lever 

ragtime 

physical valuation of R.R. 

score (in music) 

commercial fertilizer 

Magna Charta 

voucher 

ohm 

string halt 

fourth dimension 

piston rod 

Pythagorean proposition . . 

single tax 

stamen 

hemstitch 

Spanish Armada 

statute of limitations 

coherer 

vertebrate 

parallelogram 

omelette 

Reichstag 

Commerce Court 

states' rights 

space bar 

giblets 

Australian ballot 

mollusk 

perspective 

fireless cooker 

mortgagee 

referendum 

Formosa 



21 



15 



9 
15 



21 



IS 



Total . 



F. of A. (obtained in next question) 

•57Xtotal 

.8 times the grade 



144 



82 



27 

15 

9 

15 

3 



12 



30 
3 



18 



30 
15 



18 
24 



3 
15 
12 



96 
55 



426 
243 



66 44 194 



Special Tests and Their Significance 



59 



Answer to question 10: 



Definitions of terms: 

a. simile 

b. cube root "When a number is multiplied 

by itself three times." 

c. improper fraction 

d. rag-time — "music that is used in songs 

and vaudeville." 

e. physical valuation of railroads 

f. commercial fertilizer — "Fertilizer that 

is used in a commercial way." .... 

g. ohm 

h. Pythagorean proposition 

j. single tax 

j. hemstitch — -"In sewing when threads 

are drawn out and then 4 or more 
drawn together in the centre." 

k. vertebrate — "The small parts that 

make up the back bone." 

1. parallelogram — "A figure where oppo- 
site sides are parallel." 

m. omelette — "A dish made from eggs." .. 



Sum 

Factor of accuracy 15 ^ = 



10X.57. 
-50X.57. 
-20X57. 



27 



57 



Grade given 

by 



pupil 




27 



Mi -(-mean (mean in question = 16) 
Ei+mean ( " " " =15) 

Hi -(-mean ( " " " =22) 

or Mi = 4 
Ei = 5 
Hi = 10 



grader 


2 

1 

2 









3 

2.5 



15.5 



-29 



100 
20 



197 



20 



-11 
324 



32 



60 



Educational Guidance 



In the following sample only the detailed grading is given where the judgment 
of the grader is involved : 



Name (Pupil No. 14). 



Date. 



Question 1. 

Combination of all the magazines, except 

that one marked "A." (56) 

A, Life (See question 2) (10) 



66 



Grade of 

Same foe 



Factor Con- 
tributing 
to Total 
Grade 



M 



E 



160 
30 



190 
2.9 



H 



113 
1.7 



Average grade 

33 Xaverage grade 

Question 2. 

"I enjoy it because it is humorous and has some very in- 
teresting comments on the important things which are at- 
tracting attention." 

The interest here shown in current events warrants the in- 
crease in the history grading of Life, so, for this individual, 
the magazine is graded 3 for history instead of 1. 

Questions 3-9. 
Sum of the grades for questions 3 to 9 inclusive 



Mi Ei Hi 



96 



59 39 



56 



135 



Special Tests and Their Significance 
Question 10: 

Terms and definitions of same 



61 



a. simile "A simile is a certain kind of a 

sentence." 

b. cube root — "I can't explain." 

c. improper fraction — "is a fraction which 

is not proper." 

d. ragtime — "A form of music with no 

special time." 

e. physical valuation of railroads — ' ' Know 

nothing about it." 

f. commercial fertilizer — "Know nothing 

about it." 

g. ohm — "Can't explain." 

h. Pythagorean proposition 

i. single tax — "A tax on your personal be- 
longings." 

j. hemstitch — "A certain kind of stitch. 

Can't explain." 

k. vertebrate — "Know nothing about it." 
1. parallelogram — "A figure. I can't ex- 
plain." 

m. omelette — "Can't explain." 



Factor of accuracy = .66 

10X.66 

-50X.66 

-20X.66 



Grade for 

same given 

by 



Pupil 

1 
2 

2 

3 



1 
1 

1 



16 



Mi+mean (mean in question = 18) = 
Ei -j-mean (mean in question = 17) = 
Hi -fmean (mean in question = 26) = 
or Mi =—5 
Ei=-7 
Hi = -8 



Grader 

1.5 
1 

1.5 

1.5 




1 
1 



10.5 



-33 



66 
13 



102 



10 



-15 
176 



18 



62 



Educational Guidance 



The following sample covers determination of the factor of accuracy only: 



Name (Pupil No. 158). 



Date 



a. simile — "A comparison." 

b. cube root — "A quantity multiplied by itself then into 

the product produces a certain cube." 

c. improper fraction — "A fraction whose numerator ie 

larger than its denominator." 

d. ragtime 

e. physical valuation of railroads — "Actual value of 

material and construction." 

f . commercial fertilizer 

g. ohm — "A certain degree to which magnets are wound." 
h. Pythagorean proposition — "Proposition discovered 

by Pythagoras regarding squares over the sides of 
rectangular triangle." 

i. single tax — '"Tax on land only." 

j. hemstitch — "An open kind of stitch used in sewing." 

k. vertebrate — "An animal having a skeleton." 

1. parallelogram — "A figure having two pairs of parallel 

sides." 

m. omelette — "A preparation made with milk and eggs." 

Factor of accuracy = 33/32 = 1.03 



Grade for Same 
Given by 


Pupil 
3 


Grader 
3 


2 


3 


1 
3 


3 
1 


3 

3 


3 

2 


3 
2 
3 
3 


3 
3 
3 
3 


3 
3 


3 
3 



32 



33 



The grading of this interest test is not as long or difficult a 
task as it might at first seem. It can be greatly expedited by 
grading one question at a time after having memorized the table 
pertaining to that question, except the table for books, which it is 
impracticable to attempt to memorize. The use which is made 
of the interest test grades as well as the grades of the other tests, 
is given in the following section. 



Combination of Grades of Various Tests for Purposes 

of Prognosis 

Taking the grading of all the tests, there are six measures for 
each individual as follows: M t , mathematics test, which is 
either the algebra or the geometry test; E t , English test; H t , 
history test; Mi, Mathematics interest test; E b English interest 
test; and Hi, history interest test. Not only do the gradings of 
each of these tests have significance in connection with the sub- 
ject for which they are specifically graded, but they also have 
some significance for other courses. In other words, the most 
probable first-year grade in English may be said to be a function 



Special Tests and Their Significance 63 

of M t , E t , H t , M ; , E ; , Hj. The regression equation, expressing 
E as a function of these six variables, might be calculated, but 
the labor would be very great, and therefore a slightly different 
method has been used, probably with little loss in the degree of 
correlation. The regression equation expressing E as a function 
of M t , E t , and H t , is calculated, and this particular function is 
called E ct (meaning the measure that represents that combina- 
tion of the tests M t , E t and H t , which correlates the most highly 
with English). A second regression equation expressing E as a 
function of M b Ej and Hi, is also calculated and designated as 
E ci (meaning the measure which represents that combination of 
the interest tests Mj, E; and H;, which correlates most highly 
with English). Finally a regression equation is calculated ex- 
pressing E as a function of E ct and E c i, and this function is 
designated as E c (meaning the measure which represents that 
combination of E ct and E ci which correlates the most highly 
with English). So far as English is concerned, the entire object 
of the tests has been the derivation of this measure, E c ; and the 
correlation between E and E c establishes the extent to which 
grades in the tests given serve as a basis for the prognosis of 
ability in high school English. The same procedure is followed 
with reference to mathematics and history, leading to measures 
M c and H c . The following sections will be devoted to explaining 
the derivation of M ct , E ct , H ct , M ci , E ci , H ci , M c , E c and H c , in 
the order named. 

M ct — Combination of Tests with Reference to (a) Algebra 
and (b) Geometry 

(a) Algebra: In order that it may not be lost sight of, it is 
repeated here that all of the measures mentioned in the last 
section are measures that are expressed as deviations from the 
means of the groups to which the measures belong. For one 
duplicating this test, the means given on page 68 may be assumed, 
or better, they may be calculated anew for the group tested. 

The combination A ct , of A t , E t , H t , which correlates the 
highest with A is as follows : 1 

A ct =.6A t +.4E t +.llH t 

This equation is self explanatory. To obtain A ct it is only 

1 See Appx., p. 99. 



64 Educational Guidance 

necessary to add .6 of A t , .4 of E t and .11 of H t , paying proper 
attention to sign. The correlation between A and A ct equals .48. 
The apparent weighting of the three tests, .6, .4, .11 is not the 
exact weighting of the tests, for the standard deviations affect 
these regression coefficients. Since the standard deviation of 
H t is large the weighting is somewhat greater than .11. The 
weighting seems very reasonable, bearing in mind that H t is 
not as reliable a measure as E t as it has but a single measure 
entering into it, whereas E t is an average of three. 

(b) Geometry: The regression equation for geometry is: 

G ct = .8G t +.08E t +.184H t 

The correlation between G and G ct equals .43. The small 
weighting of E t is somewhat of a surprise. It must be assumed 
that some of the elements entering into the grading E t are more 
directly related to algebra than to geometry. 

The measures A ct and G ct are entered in the same correla- 
tion tables and designated as M ct , for purposes of determining 
the relative weighting of mathematics, English and history tests. 1 

E ct — Combination of Tests with Reference to English 
That combination of M t , E t , H t which proved the most feasible 



is: 



E ct = i(M t +E t +H t ). 



The correlation between E and E ct equals .46. The weighting 
here used yields a correlation practically as high as that given 
by the regression equation but this is not an accurately deter- 
mined regression equation and it is impossible to use it for deter- 
mining the relative importance of the factors M t , E t and H t with 
reference to E. It may, however, be said that they do not differ 
greatly in their relative bearing upon E. 

H ct — Combination of Tests with Reference to History 

The combination for history is the same as that for English : 3 
H ct = |(M t +E t +H t ) 



1 See Appx., pp. 99, 105. 
1 See Appx., p. 100. 
3 See Appx., p. 100. 



Special Tests and Their Significance 65 

No accurate analysis of the importance of the factors M t , E t and 
H t with reference to their bearing upon history is possible from 
this datum. 



M c i — Combination of the Interest Tests with Reference to 
Mathematics 

The regression equation giving that combination of Mj, E, 
and Hi which correlates the highest with M is : 

M ci = .5M i -\-ME i -.2¥L l 

The correlation between M and M cL equals .30. The mathe- 
matics interest test is weighted the most heavily in this equation 
in spite of the fact that the coefficient of E 4 is the largest. This 
comes about from the fact that the standard deviation of E 4 is 
considerably smaller than that of M;. The actual weighting 
of the different elements is approximately in the ratio of 224: 
183: — 95. The occasion of the negative weighting of the history 
interest test may be determined from the raw data for the calcu- 
lation of the regression equation given in the Appendix. 1 In 
brief it is due to the low correlation between M and H u .15, 
and the high correlations between Mi and H,, .54, and between 
Ej and Hi, .63. Why the first of these three correlations is low 
and the second and third high is not apparent — an accurate 
calculation of the regression equation involving the parts of the 
interest test would reveal the cause, but it would be a very labo- 
rious task. 

E ci — Combination of the Interest Tests with Reference to English 

The regression equation giving that combination of M l} ~E„ 
and Hi which correlates the highest with E was found to have 
only a trifling advantage over the use of E ; alone. 2 
Therefore the relation used is: 

E C i — Ei 
The correlation between E and E ci equals .46. 



1 See Appx., pp. 103-104. 

2 See Appx., p. 104. 



66 Educational Guidance 

H ci — Combination of Interest Tests with Reference to History 

The regression equation giving that combination of Mi, Ej, 
and Hi which correlates the highest with history is : x 

H ci =-.5Mi+.38Ei+.7Hi 

The correlation between H and H c i equals .33. The negative 
weighting of Hi in its bearing upon mathematics is comparable 
to the negative weighting here, of Mi in its bearing upon history. 
The data for definitely determining the cause of this latter, as 
well as the former, are lacking. 

M c — Combination of M c i and M ct with Reference to Mathematics 

The regression equation giving that combination of M c ; and 
M ct which correlates the highest with mathematics is : 2 

M c = .66M ci +1.00M ct 

The correlation between M and M c differs somewhat for the 
pupils taking geometry from that for the algebra pupils. The 
correlations are: r GGc = A4, r AAc = .49. These correlations are 
not as high as could be desired, nor as high as the correlation 
between grammar grade mathematics and first year mathematics, 
which is .58. However, r^ is only .09 less than t"f m (7, 6, 5, 4 M )> 
and when it is considered that the former is a correlation based 
upon tests of a few hours duration while the latter is based upon 
the work of four years, it is a very satisfactory showing and is of 
positive value for purposes of prognosis and classification. 

Lacking information as to the pupil's past performance, classi- 
fication, at present, usually depends upon such things as the 
pupil's^or teacher's, preference as to the hour when the subject 
is to be taken, or upon the first letter of his last name, or some 
other equally irrelevant point. It is earnestly hoped that tests 
will be devised enabling a very accurate prognosis, but, pending 
such tests, there is nothing to lose and everything to gain by the 
use of the tests here given, whose significance has been accurately 
evaluated upon the basis of the performance of some 235 pupils. 
A summarized statement of the procedure in using the test data 
is given on page 68. 



1 See Appx., pp. 104-105. 

2 See Appx., p. 105. 



Special Tests and Their Significance 67 

E c — Combination of E ci and E ct with Reference to English 

E ci and E ct have equal significance in determining the most 
probable standing in English. The regression equation is: 

E c = E C i+E ct 

The correlation between E and E c is equal to .55. This correla- 
tion is higher than the correlation just above, for mathematics, 
though considerabley less than r FE(7i 6i 5> 4e) , which equals .71. 
It is interesting to note that whether dealing with grammar 
school grades or with special tests it is possible to give a closer 
estimate of a pupil's performance in English than it is in mathe- 
matics. The greater difference between the natures of algebra 
and arithmetic, than between high school English and elementary- 
school English, is probably a contributing cause in the case of 
these special tests as well as in the case of elementary school 
records. 

H c — Combination of H c ; and H ct with Reference to History 

The regression equation giving the best combination of H ci 
and H ct with reference to history is: 

H c = .4H oi -|-H ot 

The correlation between H and H c equals .49. The apparent 
unimportance of H ci in comparison with H ct exists only in part, 
as the standard deviation of H ci is much larger than that of H ct . 
The actual relative weighting of H ci and H ct is approximately 
in the ratio of 22:39. 

Use of Regression Equations 

Substitution of the test grades in the regression equations is 
required in order to use them for purposes of estimation of prob- 
able high school standing in the subjects, algebra, geometry, 
English and history. After having given and graded the tests 
for the pupil whom it is desired to examine the grades are sub- 
stituted in the equation giving A c , for purposes of estimation of 
his probable standing in freshman algebra, in the equation giving 
E c , for estimation of his probable English standing, etc. The 
necessary equations are here summarized: 



68 



Educational Guidance 



M c = A c orG c . 

A c = .66M ci +M ct = .33M i +.44E i -.132H i +.6A t +.4E t +.llH t . 
G c = .66 M ci + M ct = .33 Mi + .44 Ei - . 132 Hi + .8 G t + .08 E t 
+ .184H t . 

E c = E ci +E ct = Ei+HM t +E t +H t ). 

H c = .4H ci +H ct =-.2M i +.15E i +.28H i +KM t +E t +H t ). 

M ci = A ci or G ci = .5M i + .65E i -.2H i . 

E ci = Ei. 

H ci =-.5Mi+.38Ei+.7Hi 

M ct = A ct or Get. 

A ct = .6A t +.4E t +.llH t . 

G ct = .8G t +.08E t +.184H t . 

E ct = KM t +E t +H t ). 

H ct = E ct . 

Mi = A i0 r G i = i(2M Spts +.5M Ellts +4Mvoc 8 +10F of A+.8M Wds 
— mean) . 

Ei = .l(2E S pt 8 +.5E Ents +4Evocs-50F of A + .8E Wd8 +33E Maga 
+ 1.65E Bks — mean). 

Hi = .l(2Hspt a +.5H Eat3 +4Hv OC s-20F of A + 8E Wds +33E Mag3 
+ 1 .65 Eaks — mean) . 

M t =A t orG t . 

A t = ^(Sum of grades of all the problems — mean) . 

G t = ^(Sum of grades of problems 1, 7, 8, 9, 10 — mean). 
. E t = f(E a +E v +W-mean). 

H t = 2 (H a — mean) . 

To obtain any of the last eight grades subtract the mean from 
the pupil's gross mark and divide the remainder by the divisor 
given in the equations and repeated in the following table of 
means and divisors. 



Group and 
Class 

1 Beginning 2d 

year . . 

2 Mid-year 1st 
year . . 

3 Entering 1st 
year . . 

4 Beginning 2d 

year . . 

5 Entering 1st 
year . . 



Math. 
Test Mt 


Eng. 

Test Et 


Hist. 
Test Ht 


Math. 
Int. Mi 


Eng. 
Int. Ei 


His 
Int 


OQ 

a 

2 


GO 

S-! 

> 

ft 


a 


02 
m 
> 

Q 


CD 
C 

o3 


OQ 
U 
OQ 
> 




on 

GQ 
> 

Q 


CO 

a 


m 
S-t 


m 

a 

0J 
2 


Gt25 


3 


18.5 


3/2 


7 


1/2 


95 


5 


170 


10 


260 


At89 


5 


16 


3/2 


6 


1/2 


80 


5 


150 


10 


220 


i At72 


5 


15 


3/2 


6 


1/2 


65 


5 


160 


10 


200 


Gt26 


3 


19 


3/2 


5.5 


1/2 


100 


5 


190 


10 


280 


At88 


5 


17.5 


3/2 


6.5 


1/2 


70 


5 


170 


10 


240 



> 
Q 

10 

10 

10 

10 

10 



Special Tests and Their Significance 



69 



If A represents the most probable algebra grade expressed as 
a deviation from the mean, for some given numerical system of 

marking it is related to A c as follows : A = Taa — A c = .49 - — — A 

c <ta c 3.736 

in which A c is given for each pupil by the tests and ca is to be 
determined for the school in question. If the grading is on a 
percentile scale with a passing mark of 70, <r A will be in the neigh- 
borhood of 8. The following are the standard deviations of the 
type <r Ac . 

<r Ac = 3.736; er Gc = 4.066; <r Ec = 5.328; <r H<i = 3.622. 

If G, E, and H have similar meanings to A, their values are as 
follows : 



G = .44 



-^-G e ; E = .55-^-E c ; H = .49-^-H c 
4.066 5.328 3.622 



The calculation may be presented as follows: 



Gross Grade 


OF 


Pupil 


Group 3 


Alg. 


test 




71 


Eng. 


test 




22 


Hist 


test 




9 


Math, int 


test 


68 


Eng. 


int. 


est 


153 


Hist 


int. 


test 


141 





Devia- 




Means 


tions FROM 

Mean 


Divisors 


72 


-1 


5 


15 


7.5 


3/2 


6 


3 


1/2 


65 


3 


5 


160 


-7 


10 


200 


-59 


10 



Deviations 
-f- Divisors 

= At or Mt 

5 = Et 

6 = Ht 
l=Ai or Mi 

-l=Ei 
-6 = Hi 



Substitution of these values in equations M c , E c , H c gives 
A c = 4, E c = 3, H c = 2. If these measures are divided by their 
respective standard deviations (o"a c = 3.736, <te c = 5.328, o"h c = 
3.622), the resulting measures, 1.070, .563, .552, express the 
predicted standing in terms of the standard deviation. 

The calculation carried through is typical, being in fact that of 
pupil No. 157, and it is to be noted that the prediction is quite 
selective, for the estimate for algebra, 1.070, is one-half a standard 
deviation larger than the prediction for English. The advan- 
tage of such a differential prognosis over one of average ability 
only is very evident, if classification of the pupil is the aim. 
The extent to which the method performs this differential 
diagnosis may be measured by taking the differences between 
measures such as 1.070 and .563 and correlating them with the 
actual differences in grades in mathematics and English courses, 



70 Educational Guidance 

these latter likewise expressed in units of the standard deviations. 
This correlation may be expressed by the symbol r(M-E)(M -e^ 
and calculation gives its value to be .31. This correlation 
is far from negligible and indicates the selective nature of 
ability. It may be expected that further use of the same 
method will lead to higher correlation and to very valuable tests 
for purposes of differential diagnosis. 

The scheme just given for evaluating the record of any one 
pupil is a rather long process. It will be found that there is a 
very great saving in time if the work is tabulated and the steps 
performed one at a time upon the entire number of pupils' rec- 
ords, rather than as in the example, where the steps were per- 
formed consecutively and in toto for one pupil before going on to 
the next pupil. 

The time of giving and evaluating the tests can be further 
shortened by omitting those parts not used in the final result. 
In the geometry test the following problems may be omitted: 
2, 3, 4, 5, 6. In the English and history tests omit the grading 
for dramatization, and in the history test omit the grading for 
valuation. It is, however, recommended that in the interest 
test a larger number of words be used in determining the factor 
of accuracy. 

It will at times happen that test records for a given pupil are 
incomplete, in which case a zero may be put in for the missing 
record, without greatly lessening the significance of the measure. 
It would be a little more reliable to estimate closely, from the 
data at hand, the probable value of the missing record and enter 
it, but there is danger that the estimate will be quite inaccurate, 
in which case it is worse than no estimate at all. The assigning 
of a zero grade is simply assigning the mean grade. 



SECTION 6.— USE OF ALL SOURCES OF DATA IN 
ESTIMATING PROBABLE AVERAGE STANDING 

Of the group of pupils whose elementary school records were 
available 33 were entering first year of high school. All of the 
following data were available with reference to these 33: (1) 
average first-year grade, F A ; (2) elementary school grade (7, 6, 5, 
4a); (3) teachers' estimates, Est A ; (4) special tests M c , E c , and 
H c . The special tests are arbitrarily combined into a single 
measure by averaging, 

M c +E c +H c 

3 =Ta - 

To determine the total bearing of these four sources of data 
upon average first-year standing the regression equation com- 
bining them with reference to it has been calculated from the 
data in the accompanying table. 

It is to be noticed that here F a ( 7 > 6 » 5 > 4 a) Est A 

rF A (7,6,M A ) = .83>.789 (given (7,6,5,4 A ) .83 

on p. 8), and that r F Est = 



Est A .81 .68 



T A .51 .56 .54 

.81 > .76 = ^Av(I.a., r Cons.,Emo.i.,Exp.). 

(Given on p. 16). These differences are probably entirely 
accounted for by fluctuations due to sampling. The smaller 
values are the more reliable, being based upon larger populations. 
The regression equation is * 

F A = .536 (7, 6, 5, 4 A ) + .481 Est A -.043T A . 

The negative regression coefficient, — .043, is probably due to 
fluctuations in sampling. The probable error of the partial 
correlation coefficient entering into this regression coefficient is 
.112, so that no great significance can be attached to its negative 
value. 

r F [(7, 6, 5, 4 ),Est t ] = .89, with a probable error of .023. 
This very high correlation is of interest in showing the great 
stability of individual character. To know that a pupil's grades 



x See Appx., p. 106. 

71 



72 Educational Guidance 

in the first year of the high school are so largely determined by 
what he possesses within his own personality is convincing 
evidence of the paramount importance of nature over and above 
nurture. With the undoubtedly varying environments under 
which these pupils lived there would be a greater divergence 
between estimate and accomplishment if nurture were the major 
factor. 

There is a likelihood that the correlation of .89 is higher than 
might be ordinarily expected from similar data, for, as noted, 
the particular sample dealt with seems to show a slightly closer 
relation than usual. This is true to the greatest extent in the 
case of teachers' estimates, where it is likely that the teachers 
who made the estimates were particularly well acquainted with 
the pupils, for these pupils had been in the elementary depart- 
ment of the same school for the preceding four years, and their 
capacities for accomplishment were probably very well known. 
The lack of absolute independence between teachers' estimates 
and average class standing, noted on page 15, is a factor to be 
borne in mind. 

In case it is essential to obtain as close an estimate as possible 
of a pupil's ability all three sources of data could profitably be 
used, but for ordinary needs of classification one source should 
be adequate. The method of combining the three measures into 
a single measure is given in the Appendix, p. 106. 



SECTION 7.— THE AGE OF PUPILS AS A FACTOR 

The number of factors involved in this study has been so 
great that the age factor has been omitted. 

The correlation between average class standing and age, using 
all the data, is —.31. Eliminating the bearing of innate mental 
capacity (or mental capacity as existing at one certain age) 
would certainly give a positive partial correlation between age 
and standing in a given grade. Though it is a fact that the aver- 
age twelve-year-old first-year pupil has a higher average standing 
than the average sixteen-year-old first-year pupil, it of course is 
not true that the average twelve-year-old is brighter than the 
average sixteen-year-old. 

The occasion of the negative total correlation, —.31, is prob- 
ably due to the fact that dull and over-age pupils are advanced 
more rapidly than their talents warrant, thereby always keeping 
them in a class which taxes their capacities and in which they 
can secure only low marks. 

Since there exists this negative correlation between age and 
average standing in a given grade, the use as a measure of in- 
telligence, of the age at which a pupil reaches a certain grade, 
gives to the bright pupil but part of the credit due him. The 
bright pupil is less advanced, and the dull pupil more advanced, 
judged by the grade attended, than talent warrants. The 
effect of this is to make the measure "age of attaining a certain 
grade" less reliable as a measure of ability than it otherwise would 
be. 



73 



SECTION 8.— COMPARISON WITH OTHER STUDIES 

The most fundamental distinction between this and the great 
majority of correlation studies is that the aim of this study is 
prognosis and not at all to establish the existence and magnitude 
of some theoretical relationship. This fact has already been 
referred to but is mentioned again as some important points of 
method depend upon it. It will be noted that, in the following 
paragraphs, where comparison with other investigations of 
mental relationships is impossible, it is generally due to difference 
in method, necessitated by this difference in purpose. 

A number of investigations, notably several by Spearman and 
his pupils, have as their object the determination of the abstract 
relationship which exists between certain tests and mental 
capacities. The aim is to establish the relationship that exists 
after errors of sampling, observation, and the like have been 
eliminated. The direct conclusions from such studies are of 
necessity theoretical, whatever may be the indirect practical 
implications resulting therefrom. Acting upon these implica- 
tions educational practice might be altered, but it still would 
remain to be seen if it were bettered thereby. 

This is not a criticism of theoretical investigations for, by 
suggesting relationships and methods, they have been the fore- 
runners of progress; but it is for the purpose of pointing out the 
difference in object and the consequent difference in method 
between such investigations and the present one, which has as 
its object the utilizing of measures obtainable under ordinary 
class-room conditions, with whatever errors may be inevitable, 
for whatever they actually demonstrate themselves to be worth 
as evidence of the capacity it is desired to measure. 

If one set of test measures correlates with class standing to a 
certain extent, no amount of superimposed treatment for elimi- 
nation of observational errors, chance errors, or the like can 
change this raw relation which exists. Correction for atten- 
uation would lessen the accuracy and vitiate the significance of 
the use of marks as a prognosis of other " raw" marks. Knowing 
the correlation between tests and average standing and wishing 
74 



Comparison with Other Studies 75 

to estimate the latter from the former, the most reasonable 
prediction is that given by the regression equation. This is 
exactly what the regression equation has been devised to give, 
and "correction" of the correlation coefficients in any way at all 
would lead to less accurate estimation. For this reason, none 
of the studies, the conclusions of which are based upon "cor- 
rected" coefficients of correlation, are comparable with this work, 
nor should the size of the coefficients of correlation here obtained 
be compared to "corrected" coefficients. The latter are meant 
to be a prophecy of what would be the correlation provided errors 
of various kinds were absent, while the former state the relation 
between existent measures. 

The results of this study, however, do shed some light, and 
give a method of attack, upon the problem of the existence, or 
non-existence, of a single mental function which is paramount 
in all intellectual activities. The statement of the view of those 
holding to the idea of a single mental function has undergone 
much development and elaboration, until it now seems to be 
about as follows: — that every intellectual performance depends 
not only upon a general factor, "but also in varying degrees upon 
a factor specific to itself and of very similar performances." 1 

How the most ardent advocate of the specific nature of ability 
can object to such a statement, is hard to see. The problem 
is no longer a qualitative but a quantitative one. It is now 
necessary to measure intellectual performances and ascertain 
what part of each is a common element and what part is unique. 
The regression equation method, involving more than two vari- 
ables, is beautifully adapted to solving this problem, and corre- 
lation between differences in accomplishment, or capacity, gives 
first-hand testimony as to the uniqueness or generality of mental 
function. 

Pupils in the elementary school demonstrate a unique ability 
along the line of mathematics or English, by getting, relative to 
their average accomplishment, higher or lower marks in these 
subjects. That these marks do represent a unique ability and 
are not due to chance and the vicissitudes of teachers' gradings, 
is evidenced by the fact that different teachers, in the high 



1 See B. Hart and C. Spearman, General Ability, Its Existence and Nature, 
British Journal of Psychology, 1912. Also C. Spearman, Theory of Two 
Factors, Psych. Rev., Vol. 21, No. 2. 



76 Educational Guidance 

school, recognize the same relative superiority or inferiority in 
the one subject, or other. The correlation r( PM _ B )( 7f6f5t 4 M . E )==.52, 
with a probable error of .065. The size of the probable error 
precludes the possibility of the correlation being due to chance. 
The alternative is that intellectual function is specific, unless it 
is argued that ability to secure grades is not solely an intellec- 
tual function. 

This might be maintained, but grades have been used by 
proponents of the general factor theory as measures of intellect; 
and, furthermore, if so fundamental a mental characteristic as 
the ability to earn grades is not a fit capacity for consideration 
in connection with the general factor theory, then the theory 
must be of very limited scope in its application, and the traits of 
importance for scholastic and business success will lie outside 
its realm. The same conclusion may be drawn just as con- 
vincingly from the correlation ^m-exmc-Ec^-SI, for its pro- 
bable error is only .040. 

Another requirement of method is that the means used in the 
study shall be capable of determination at the time of prognosis. 
Studies which have dealt with the correlation between high school 
and university marks, or between elementary school and high 
school marks, have, without exception so far as the author is 
aware, selected the group upon the basis of attendance in the 
higher school, and then calculated the means in the lower school 
of the group thus selected. It follows that the means used for 
the lower school data are not capable of determination until the 
selection has occurred upon the basis of attendance in the higher 
school. Any elimination that takes place is entirely obscured 
by the method, and the use of the correlation found, for purposes 
of prediction, is not sound because it is not known from what 
mean, deviations should be measured. 

However, though theoretically justified this criticism is prob- 
ably not of very great moment when dealing with elementary 
school and first-year high school pupils. The evidence of this 
study is that there is not a sufficient selection of the brighter 
pupils in passing from the elementary school to the high school 
to necessitate changing the elementary school mean of pupils 
who attended high school from the mean of elementary school 
pupils in general. It is quite possible that this would not be 



Comparison with Other Studies 77 

true in schools where there is a greater elimination than in the 
well-to-do schools from which these data are obtained. 

The study of Dearborn 1 is excellent evidence that high school 
efficiency is highly correlated with university proficiency, but 
the method is not a serviceable one for a quantitative prognosis 
problem; and the high school means in his distributions are 
means of high school pupils who later attended college and are 
therefore the means of a selected group. 

The same remark may be made in regard to the means used 
in the study by Miles 2 and it may be a material point in this 
case, for the amount of elimination between the elementary 
school and the fourth year of the high school is very much more 
extensive, and probably also selective, than between the elemen- 
tary school and the first year of the high school. Miles finds 
that the correlation between the average elementary school 
grade and the average high school grade is .71. This is quite in 
harmony with the results of the present study and it is probable 
that Miles' data, treated by the regression equation method, 
would yield correlations between .80 and .90. 

The fact that Miles deals with the average of all high school 
grades results in higher, or lower, correlations than would be 
obtained in dealing with first-year high school marks only, 
dependent upon which of the two following factors is the stronger : 
(1) In general, as the time between testing is increased the 
correlation decreases; and as the second, third and fourth years 
of the high school are more and more remote from the elementary 
school in time, it might be expected that correlation between the 
elementary school record and the first-year record would be 
greater than that between the elementary school record and the 
average of the entire high school record. (2) A factor tending 
to offset this is the fact that the reliability of an average increases 
as the number of grades entering into it increases, and, to the 
extent that a grade represents native ability, the greater the 
number of grades averaged the greater the reliability of this 
measure. It is impossible to say, a priori, which of these factors 
is the more important, but it is the author's opinion that the 



2 See Dearborn, W. F., Relative Standing of Pupils in the High School and 
in the University, Wis. Univ. Bulletin, No. 312, 1909. 

2 See Miles, W. R., Comparison of Elementary and High School Grades, 
Univ. of la. Studies in- Education, Vol. 1. No. 1. 



78 , Educational Guidance 

importance of the second factor has been, quite generally, under- 
valued, and might easily be the more important of the two. 

Another class of studies has been undertaken, especially in 
England by investigators who have found the correlations be- 
tween various tests and intellectual ability — the latter based 
upon teachers' and headmasters' estimates. It is pertinent to 
ask what relation there is between intellectual ability and the 
ability to secure grades. 

The regression equation giving the bearing of teachers' esti- 
mates of intellectual ability, conscientiousness, emotional in- 
terest, and oral expression, upon average class standing, weights 
these factors in the ratio of 8:4:2:1, or, combining the first and 
last and designating it as the intellectual factor, and combining 
the second and third and designating it as the motive factor, or 
factor of effort, it is seen that the weighting is in the ratio of 3 :2. 
Since effort is so important a factor in accounting for the ability 
to secure grades, it is apparent that the correlation between tests 
and intellectual ability will be quite different from, and probably 
higher than, the correlation between the same tests and class 
standing. This is a common finding and in the study by Wyatt 1 
it is possible to estimate the extent of this difference. 

Wyatt finds that the average correlation between his tests 
and intelligence, as determined by the headmaster's estimate, 
averaged .63, and that the correlation, for a different group, 
between the same tests and intelligence, as judged by class stand- 
ing, averaged .51. As the headmaster did not grade upon both 
intellectual ability and effort it is probable certain evidence of 
excellent effort received credit as intellectual ability. Accord- 
ingly it may be expected that the difference in correlation be- 
tween Wyatt's tests and real intellectual ability, from that be- 
tween his tests and class standing, is actually greater than the 
.12 found. 

Wyatt's tests apparently were given at about the same time 
that the marks which determined class standing were earned, so 
that his results are not comparable with the results of this study. 
Also the age of pupils is different, but his results suggest that 
certain of the tests used, especially the analogy and completion 
tests, are highly indicative of average class standing, and tests 

1 See Wyatt, S., Quantitative Investigation of Higher Mental Processes,, 
Brit. Jour, of Psyc, Vol. VI, Pt. 1. 



Comparison with Other Studies 79 

of this nature are worthy of investigation for purposes of esti- 
mating average capacity, but it is doubtful if they have par- 
ticular value for purposes of differential prognosis. In giving 
such tests it is not to be expected that the care with which Wyatt 
gave them will be duplicated under ordinary class conditions. 

There are at least two classes of tests which are comparable 
with the tests here given, so far as purpose is concerned. One 
of these is entrance examinations. They perform their task, in 
the main, by attempting to measure acquired knowledge, whereas 
the tests here given, in the main, attempt to measure interest 
and capacity. Both types of examinations have a function to 
perform and the former should be supplemental to the latter in 
the final determination of the classification of the pupil. Acquired 
knowledge tests, of themselves and alone, are too likely to be 
evidence of the degree of success which has attended a cramming 
process, and not very definitely evidence of ability, which is the 
more important consideration. The following correlations, 
given by Thorndike, 1 show a progressive decrease in correlation 
between the median entrance examination grade and the average 
grade in the different years of the college course; freshman year 
.62, sophomore year .50, junior year .47, senior year .25. In- 
tellectual capacity could hardly have changed much, relatively 
from pupil to pupil, during the four years of the college course. 
These correlations seem to indicate that the capacity measured 
by the entrance examination was, in the main, acquired knowl- 
edge and not intellectual ability, otherwise, why the decrease 
from year to year? 

For purposes of immediate differential diagnosis tests of ac- 
quired knowledge undoubtedly perform an important function, 
but for the broader problems of vocational guidance and the 
selection of general courses of study they have very limited 
scope. 

The second class, tests of the Binet type, have classification 
as their object, and in this respect are comparable to the tests 
here given. Thus far, however, they have not shed much light 
upon the points of relative strength or weakness of the individual 
tested. If mental deficiency is not general, but selective, an 
individual being normal in one capacity and quite defective in 

1 See Thorndike, E. L., in Science, N. S., Vol. XXIII, p. 839. 



80 Educational Guidance 

a second, then a mass test of mental age gives no light upon the 
distinctive feature which it is desirable to be acquainted with. 
There is plenty of evidence to indicate that deficiency is selective 
in many cases and the defect of the Binet tests on this point 
should be remedied. However, there is sufficient correlation 
between defects to make a Binet test of considerable value for 
purposes of classification; just what value has never been deter- 
mined, so far as the author is aware, in quantitative terms, i.e., 
in terms of the correlation between capacity, as estimated from 
the test, and capacity as determined by as complete and con- 
clusive measurements as possible. It is essential that mental 
age tests be tested by such methods, in order to judge which are 
the more accurate and what their accuracy is. 

The use of tests of this nature as a guide to classification may 
be illustrated by the work of Adler, in New York School 77. l 
Boys in the first and fourth grades were tested with Dr. Goddard's 
1911 revision of the Binet tests, with additions from the tests 
of Terman, Whipple and Courtis. In both the first and fourth 
grades the 35 pupils, out of about twice that number, who 
tested highest, were placed in an advanced class. The results 
were highly satisfactory. To quote the results in the case of 
the advanced section of the fourth grade: " Twenty-two of the 
thirty-five pupils are ready to begin the second half of the fifth 
grade work. Thirteen of the pupils begin the regular fifth grade 
work, though several of these will probably catch up with the 
advanced pupils before the end of the term. One pupil, who was 
absent because of contagion, will be retarded." The tests are 
evidently of high significance, but the calculation of the coeffi- 
cient of correlation between them and the accomplishment in 
class would be of value in giving a quantitative measure to the 
degree of accuracy of the classification. 



'See Adler, Martha, Mental Tests as a Basis for Classification, Jour, of 

Educ. Psych., Vol. V, No. 1. 



SECTION 9. — PRACTICAL APPLICATIONS IN HIGH 
SCHOOL CLASSIFICATION 

There can be little question as to which of the three sources of 
estimate of a pupil's scholastic ability is the preferable one to 
use, in case it is not desired or possible to use all of them. The 
elementary school records of the pupils give the most accurate 
estimate of average class standing, as well as of standing in 
specific courses. A higher correlation than .80 between estima- 
tion and actual first-year standing should not be demanded, or 
expected, in a correlation of this nature. 

There would be a great advantage in having a uniform record 
card, for each state school system, to contain, in addition to 
other data, the pupil's grades from year to year, together with a 
definite statement of the significance of the grades in terms of a 
normal distribution, or as deviations from the grade mean for the 
local system in question, expressed as multiples of the variability 
for that system. If these cards were freely transferred from school 
to school, as the pupil changed, it not only would be possible to 
classify pupils accurately each year, but it would be of incal- 
culable value from other standpoints as well, for there is prob- 
ably no easily obtainable data which could compare in signifi- 
cance with such a record. 

The estimates of several of the previous teachers of the pupil 
give an excellent basis for classification, but wherever available, 
the more valuable records in the elementary school are probably 
also available, so that, for high school classification, they are 
not of prime importance. 

They are, however, of specific value in analyzing the elements 
which contribute to scholastic success. In the regression equa- 
tion based upon teachers' estimates, effort shows itself to be a 
very important factor. There would, therefore, be many advan- 
tages for educational, and even more particularly for vocational, 
guidance if there were available grades representing ability and 
effort, as well as accomplishment. 

The importance of the interest and specific subject tests is not 
6 81 



82 Educational Guidance 

to be measured solely by the extent of their correlation with class 
standing, as they probably are not at all measures of conscien- 
tiousness. Conscientiousness has been shown to be second in 
importance to intellectual ability only and to deserve a weight 
of 4 to 12 for all other factors measured, intellectual ability, 
emotional interest, and oral expression. A classification of 
pupils which does not take into account conscientiousness may 
be particularly advantageous in that it throws the indolent in 
with conscientious pupils of equal mentality, thus acting as a 
strong spur to the lazy while, at the same time, the group is 
homogeneous so far as capacity is concerned and it does not 
require a dual technique of presentation on the teacher's part 
to answer the needs of dull and bright pupils. It may be that 
in a small way a different technique of presentation is needed to 
best present a subject to a lazy pupil, from that needed in pre- 
senting it to an industrious one of the same mentality, but the 
difference does not compare with that needed in the case of dull 
and bright pupils. 

It is also undoubtedly true that the tests here given, if given 
in a high school with classes one year apart, would yield higher 
correlations than here obtained. In the school from which 
groups 1, 2, and 3 came classification is close and grades differ by 
one-half year. In the school from which groups 4 and 5 came 
particular attention is paid to classification, resulting in courses 
which fit the needs of the pupil probably fully as thoroughly as 
in the other school. In fact, in both of these schools, certain 
classes differ from each other by not more than a quarter of a 
year. The effect of this is to make the classes more homogeneous 
and such homogeneity always decreases the correlation. Ref- 
erence to the tables of means, p. 68, shows that the groups 
differ materially in their average accomplishments in the various 
tests. This shows that by means of these tests pupils could be 
classified as to their most probable place in the high school much 
more accurately than they can be classified as to their place in a 
class. The former is not the question which it is attempted to 
answer, but it is mentioned to show that the ability to place a 
pupil among all pupils is considerably greater than the ability 
to place him in a more or less homogeneous group, and as the 
groups here considered are unusually homogeneous the signif- 



Practical Applications in High School Classification 83 

icance of the tests is correspondingly greater than the correlation 
coefficients indicate. 

To make the classification still more reliable it is recommended 
that in the case of a pupil whose previous record is not available 
the tests here given be supplemented by acquired knowledge tests, 
particularly in mathematics and foreign languages. 



SECTION 10.— GUIDANCE METHODS 

It will be found that having once initiated a guidance bureau 
the demands upon it will be positive and innumerable — many of 
them extravagant. In the attempt to meet these demands, and 
to meet them on the spot and without a moment's delay, one of 
the richest sources of information is likely to be only very parti- 
ally utilized. Reference is made to that product accumulated 
by every pupil — school grades. Whatever capacity it is that a 
grade, say, in mathematics, stands for, it is measured with a 
high degree of accuracy when the records of several years and 
of several teachers are combined. A pupil's school record is the 
most complete, detailed and accurate of all records, of the 
ordinary pupil, from his entrance in school to his entrance into 
work. Unless the significance of this record is evaluated with 
reference to all the important studies and vocations the most 
readily available and accurate data concerning the applicant for 
a place in some class, or for a job, are not being utilized. The 
evaluation of these data will require much statistical work, but its 
use after evaluation is simple. 

Teachers' estimates of a pupil are second in importance only 
to grades. It requires, however, the estimates of several teachers 
to secure an accurate rating, and, under present conditions, it 
frequently is not possible to secure the estimate of more than 
one and, in cases where either the pupil or the principal changes 
location, even this is lacking. If each teacher were to place on 
record, at the end of every course, an estimate of several of the 
qualities, important for success, of each of his pupils, these data 
would be of inestimable value to the guidance expert. In this 
case, as that of school grades, a uniform record card, carrying a 
standardized grading, is essential for the best results. 

The use of special tests in vocational guidance is unlimited. 
There could well be certain specialized tests for each important 
vocation, but first of all there might be devised a general test, 
somewhat along the line of the interest test in this study, which 
would have significance in all vocations and which could be 
evaluated with reference to any one desired. This general test 
84 



Guidance Methods 85 

could test interest and general mental capacity, while it could 
be left to the specialized tests to measure specific capacity and the 
necessary acquired knowledge. 

In so far as guidance becomes a science and not an intuition, 
in so far as its method and conclusions are capable of definition 
and free use by different individuals and are not simply inner 
convictions of the expert making them, the problem of relation- 
ship, expressed in quantitative terms, between the capacity of 
the applicant and the demands of the position will become more 
and more insistent for solution. A guidance bureau should be 
like a type distributing machine, which will take a hopperful of 
type, of all the letters of the alphabet, and place each in its partic- 
ular niche, in the one place of all places where it fits. That a 
fitting distribution of human talent is a task of unmeasured 
intricacy is apparent, but the peculiar service thereby rendered 
to groping humanity makes the solution worthy the greatest 
effort. 

In broad outline, as already pointed out, the problem of vo- 
cational guidance consists of measuring the demands of the 
possible vocations, and of the capacities of the applicant and then 
fitting the applicant into that place which best suits his talents 
and his ambitions. In detailed procedure, the regression equa- 
tion method is a powerful instrument, for it enables any number 
of factors to be combined with the highest significance with 
reference to the vocation in question. When a large number of 
factors, none of them of predominant importance, contribute to 
a total result, the human intellect, unaided, cannot compass 
their total significance and it is only by mathematical means 
that they can be summed and interpreted. 



SECTION 11— APPENDIX 

Ages of Pupils 

This study covers four different groups of pupils: (1) 59 pupils starting the 
second year of the high school of School A; (2) 42 starting the second term of 
the first year of the same school; (3) 81 starting the first term of the first year 
of the same school; (4) 26 pupils starting the second year of the high school of 
School B, and (5) 25 pupils starting the first year of the high school of School 

B. Ages are expressed in years and tenths of a year from birth up to January 
1, 1913. Since the algebra and geometry tests were given during the last of 
September and the first of October, 1913, and the English, history and interest 
tests were given in January, 1913, the average ages at the times of the tests 
may be obtained from the given means by subtracting .30 of a year in the cases 
of the algebra and geometry tests and by adding .05 of a year in the cases of 
the other tests. The mean ages of the different groups January 1, 1913, is as 
follows: 

Group 1 16.1 years. 

Group 2 14.6 " 

Group 3 13.7 " 

Group 4 15.7 " 

Group 5 14.4 " 

The Assignment of Numerical Magnitudes for Literal 

Grades 

In both schools a literal grading system is in use. In School A letters A, B > 

C, D and E are used. The mark E is used very infrequently — some teachers 
not using it at all. In averaging the grades for two or more terms it was 
assumed that the difference in ability represented by grades of A and B was 
equal to the difference in ability represented by grades of B and C, etc. That 
little error resulted from this assumption will be shown in the next section of 
this appendix. In averaging the grades of four terms the following differences 
in ability may occur: 

A _A +A+A+A A1 _ A+A+A+B 

B+= A+A+B+B = A+A+A+C > A+B+B+B 

4 4 4 

£= B+B+B+B _ A+B+B+C _ ctc 

4 4 

And so on for other combinations. The literal grades thus obtained were then 
transformed into numerical grades, assuming a normal distribution of talent. 
This is very readily done by noting the percentage frequencies of the different 
86 



Appendix 



87 



grades and using such a table for transformation as that given by Thorndike 
in his " Mental and Social Measurements," pp. 221-225, second edition. Upon 
this basis literal grades were assigned numerical values as follows : 

Courses in which Tests Were Given at Beginning of Term 





















Hist. 


Hist. 


Hist. 




Alg. 


Alg. 


Geo. 


Geo. 


Eng. 


Eng. 


Eng. 


Eng. 


3rd & 
4th 
Yr. 


2nd 
Yr. 
i Yr. 


1st. 
Yr. 
i Yr. 




1 yr. 


1 Yr. 


1 Yr. 


1 Yr. 


i Yr. 


i Yr. 


*Yr. 


i Yr. 




















J Yr. 






Groups 


2 and 3 


5 


1 


4 


1 


2 


3 


4 and 5 


1 


1 


2 


A + 
M + 
A 






2.44 




1.99 














2.34 




1.42 




1.49 


2.70 


LSI 




2.23 


1.23 


1.96 


Ai- 


1.69 




.99 


















B + 


1.29 




.88 


1.56 


1.27 


1.65 


1.13 


1.49 




.55 


1.14 


B* + 


1.05 


1.92 


.77 


















B 


.80 


.96 


.51 


1.28 


.55 


.78 


.68 


.67 


1.29 


.29 


.67 


BJ- 


.57 


.44 


.23 


.92 
















c+ 


.38 


.06 


.08 


.58 


.07 


.15 


.21 


- .05 


.77 


- .05 


.28 


Ci + 


.17 


- .24 


- .08 


.15 
















C 


- .01 


- .58 


- .20 


- .36 


- .48 


- .28 


- .39 


- .70 


.32 


- .60 


- .20 


c*- 


- .24 


-1.20 


- .31 


- .71 








-1.35 








D + 


- .47 


-2.10 


- .53 


-1.00 


- .95 


- .73 


-1.13 


-1.99 


- .32 


-1.32 


- .74 


D* + 


- .64 




- .81 


-1.42 
















D 


- .77 




-1.09 


-2.16 


-1.46 


-1.11 


-1.99 




- .88 


-2.16 


-1.33 


D|- 






-1.49 


















D- 


-1.03 




-1.89 




-1.85 


-1.34 






-1.17 






E + 
E* + 
E 


-1.54 




-2.44 




-2.10 


-1.65 










-1.86 


-2.34 








-2.70 


-2.28 






-1.49 




-2.62 


E- 


















-2.23 







The same kind of transformation tables were obtained in 18 other courses 
in order to obtain numerical measures for the literal grades received in the 
first year of the high school by the 59 pupils whose records were available 
down to the third grade. The populations upon which the transformations 
were based averaged 40.4 pupils per course. 

The grades of A-f- and A|+ require explanation. In mathematics and 
English special classes were formed for the particularly bright pupils. The 
grading of pupils in these classes was more severe than the ordinary grading. 
It was the opinion of the teachers concerned that grades would be comparable 
with the rest of the grades of the school if the grades received in the special 
mathematics classes were raised one point, i.e., call C's, B's and B's, A's, etc., 
and if the grades received in the special English classes were raised one-half of 
a point. This was accordingly done, and accounts for the grades A+ and 
A|+. 

The grade D — is an average of such grades as the following : first term D, 
second term E, third term E, fourth term D. This is a passing grade for the 
year. The grade E+ is an average of the same grades, except that the final 
term is an E, constituting a failure for the year. It is reasonable to assume 
that slightly greater proficiency is shown in the former case than in the latter. 

A further simple transformation was made in order to obtain measures that 
were convenient to work with. The numerical measures obtained by use of 
the preceding transformation tables were each divided by .2 and the results 
kept to the nearest integer. The range thus obtained has about 26 divisions 



88 



Educational Guidance 



in it and the standard deviation is about 5. This distribution is very conven- 
ient for purposes of calculation and the effect of the grouping is so slight that 
no correction in the value of the coefficients of correlation need be made on 
account of it. The distributions thus obtained have means at zero, to a very 
close approximation, and no correction to the coefficients of correlation is 
necessary to correct for arbitrary means. 

To test the extent of the error due to the averaging of literal grades, the 
following facts are to be considered: 

Extent of Error in Averaging Literal Grades 

.,.,,, . A plus B t, , B plus C ~ . , 
In averagmg literal grades such as — — =B + ; = <^+, etc. 

no error is introduced because the only assumption involved is that A>B-f- 

>B, etc., which is the basic assumption underlying the transformation of 

literal grades into numerical grades. Some 92 per cent of the averaging was 

, , . t, • i i -x • x j. j ii. x A plus C B plus B D ,, , 
of this nature. It is only when it is stated that — ^— = =B that 

there is danger of error from this source. Simplifying we find that this equation 
is true only in case A— B=B— C. The following data show to how close an 
extent this assumption is true and it should be remembered that it applies to 
only about 8 per cent of the averaging done. 





Algebra-Groups 


English-Groups 


History-Group 1. 


Geometry-Group 




2 and 3. Average 


1 , 2 and 3 . Average 


Average of Two 


1. Average of 




of Two Quarters 


of Two Quarters 


Quarters 
Corresponding 


Two Quarters 




Corresponding 


Corresponding 


Corresponding 




grade: 


grade: 


grade: 


grade: 


A 


1.41 


1.80 


1.57 


2.03 




A-B = .86 


A-B=1.04 


A-B=1.05 


A-B=1.22 


B 


.55 


.76 


.52 


.81 




B-C = .71 


B-C=1.00 


B-C= .80 


B-C= .91 


C 


- .16 


- .24 


- .28 


- .10 




C-D = .86 


C-D=1.10 


C-D= .99 


C-D= .89 


D 


-1.02 


-1.34 


-1.27 


- .99 




D-E = .93 


D-E=1.27 


D-E=1.06 


D-E=1.04 


E 


-1.95 

E-F = .88 


-2.61 


-2.33 


-2.03 


F 


-2.83 









From the above table : 





If A-B = l, 


If B-C = l, 


If C-D = l, 


If D-E = l, 




thenB-C = 


thenC-D = 


thenD-E = 


thenE-F = 


Alg 


.83 


1.21 


1.08 


.91 


Eng 


.96 


1.10 


1.15 




Hist 


.76 


1.24 


1.07 






.75 


.98 


1.17 




Av 


.83 


1.13 


1.12 





Average of all = 1.02 



Appendix 
From similar tables for groups 4 and 5 : 



89 



If A-B = l, 
thenB-C = 



If B-C = l 

thenC-C- = 



If C-C-=l, 

thenC--D = 



Alg. . 
Eng.. 
Geom 
Av... 



.842 

.914 

1.070 

.942 



.679 

1.018 

.855 

.851 



.99 

.93 

.96 



Average of all = .9 18 



Similar data from the elementary school group show a still closer approach 
to equality. 

It is therefore plain that no appreciable error has been introduced by such 
averaging. 

Elementaky School Grades 

In the elementary school the system of grading for certain years was different 
from that for other years. In a few of the grades the literal system A, B, C, D, 
E, F, was used, but in the major number of grades considered the marks given 
were 1, 2, 3, — 1 being the highest grade used. By assuming a normal distribu- 
tion, and expressing both the values 1, 2, 3 and A, B, C, D, E, F in terms of 
deviations from the means, the values may be compared with each other. The 
following relation exists: 









Average 








Weighted 


English 


Arithmetic 


History 


Relation 
(Used in all trans- 
formations.) 


A to F 1 to 3 








A= 1.2<r = 1.0 


A= 1.8<r= .9 


A= 1.7<7 = .9 


A= .9 


B= .2<r = 1.6 


B= .8*7 = 1.6 


B= .5(7 = 1.8 


B = 1.6 


C=- .6.7 = 2.1 


C= .0<r = 2.1 


C=- .5<7 = 2.2 


C = 2.1 


D=-1.3<r = 2.5 


D=- .8o- = 2.6 


D=-1.4<7 = 2.8 


D = 2.6 


E=-1.7<r = 2.7 


E=-1.6(r = 3.1 


E=-2.2c7 = 3.3 


E = 3.0 


F=-2.4<7 = 3.1 


F=-2.4er = 3.6 




F = 3.4 



With this transformation table literal grades were expressed in units that 
are comparable with the numerical grading 1, 2, 3. The final grade given each 
year, for each pupil, in English is the sum of the grades given for the four 
terms of the school year in two English courses, e.g. "Reading and Literature" 
and "Composition." Thus the poorest grade possible is 24 and the best 8. 
The grades given in arithmetic and history are the sum of the grades for the 
four terms for these subjects, therefore the lowest grade possible is 12 and the 
highest 4 in each of them. 

A few of the 59 pupils in this group skipped a year. In such a case the grade 
of the year before was entered for the year skipped. This, of course, would be 
a high grade and representative of the ability of the pupil. 



90 Educational Guidance 

In expressing the grades of these 59 pupils as deviations from the means, the 
means of the grades in question were obtained. Random samplings of about 
40 from each of the grades for the various years were the basis for the calcula- 
tion of the means. The reason for this is apparent. Since this is a prognosis 
problem, the prognosis must be based upon the rankings of the individuals 
in the groups in which they are found. 

Several investigations have shown that there is a selective process operating 
to eliminate backward pupils from the grammar grades. Under these condi- 
tions, the 7th grade average of those who attend the high school would be 
slightly greater than the average of all 7th grade pupils, still more greatly 
above the average of all 6th grade pupils, etc. The difference would be most 
pronounced when dealing with the average grade of these pupils in the 4th 
grade. Calculation shows that this particular group of 59 pupils is .224 sigma 
above the average of first year pupils in general. Calculation also shows that 
they are .367 sigma above the average of 4th grade pupils. There is thus only 
the small difference of .143 sigma which can be attributed to selective elimina- 
tion of the weaker pupils. Taking all the elementary grades together, as 
combined by the regression equation, it is found that there is not even a 
difference of .143 sigma. In fact, these pupils who, as first year pupils, are 
.224 sigma above the average of such pupils are, as elementary pupils, only 
.186 sigma above the average of 7th to 4th grade pupils when grades are 
weighted according to the regression equation. If any conclusion is justified 
from this small population, it is that in this particular school there is no 
selective elimination of the duller pupils. 

In calculating the correlation between first year standing and the combined 
7th to 4th grade standing, no correction is made due to the means of the popula- 
tion of 59 being different from the means of the entire body of first-year high 
school pupils, or the entire body of 7th to 4th grade pupils. Due to the nature 
of the problem no correction to the first-year high school mean is permissible 
as the object of the study is to prognosticate divergence from this mean. A 
correction to the mean of the combined elementary grades might be applied 
but its magnitude would be .224 sigma —.186 sigma = .038 sigma, which is 
negligible. Even the correction to the 4th grade alone, .224 sigma —.367 
sigma = —.143 sigma, is inconsequential. 

The calculation of the regression equation giving the regression of the first- 
year high school grades upon a combination of 7th to 4th grade marks is based 
upon the following data: 

F A 7 A 6 A 5 A 4 A 
7 A .719 

6 A .728 .730 

5 A .531 .425 .541 

4 A .624 .551 .573 .576 

*'b 3.796 4.167 4.891 5.308 5.912 

2.250 „ % 2.250 , v 2.250 , , 2.250 , % 

FA "- 364 °i^i Pa)+-3113 — (6 A )+.1352 i ^ ( 5A )+.2419 _ (4 A ) 



F A =.3082 (7 A )+.2407 (6 a )+.0746 (5a)+.1291 <4 a ) 



Appendix 



91 



or approximately 1.803 (Fa) = §[1-667 (7 A ) +1.3 (6 A ) +.4 (5 A ) +.7 (4 A )]. Thia 
combination of elementary school records is designated as (7, 6, 5, 4a), and the 
correlation, ?t a (7, 6, 5, 4 A ) = -789. 

The same equation is used to obtain measures in elementary school mathe- 
matics and English, except that division by three is omitted, giving the follow- 
ing: 

(7, 6, 5, 4 M ) = 1.667 (7 M )+1.3 (6 M )+.4 (5m) +.7 (4 M ) 
(7, 6, 5, 4 E ) = 1.667 (7 E )+1.3 (6 B )+.4 (5 E )+.7 (4 B ) 

Calculation gives: 

rF M (7, 6, 5, 4 M ) = -580 and rp E (7, 6, 5, 4 E j = -710 

No history was taken during the first high school year so there are no history 
correlations. 

It may be noticed by reference to the preceding table that »T A 7 A aQ< i T^A. 
are less than would be expected from the other correlation coefficients. This 
may be due to the teachers of these particular 7th and 5th grades being less 
expert in estimating the ability of pupils than the 6th and 4th grade teachers. 
Whatever the cause, probably a better regression equation for general pur- 
poses can be obtained than the one given above. The accompanying curve 



r Between Grade 

in a Given Year 

and Grade One 

Yr. Before 



r Between Grade 

in a Given Year 

and Grade Two 

Yrs. Before 



r Between Grade 

in a Given Year 

and Grade Three 

Yrs. Before 



r Between Grade 

in a Given Year 

and Grade Four 

Yrs. Before 



Av. of 4 coef's. = 
.6415 



Av. of 3 coef's. 
.5753 



Av. of 2 coef's 
.541 



| 1 coef. =.624 



■ 6415- 




was drawn with this end in view. A smooth curve, not rectilinear, is drawn 
near the points representing the ordinates for the various abscissae. The 
intersections of the curve with the ordinates give the values of the correlation 
coefficients in the succeeding table. 

The falling off in correlation from year to year is thought to be reasonable 
and calculation will show that the sum of the deviations of the actual coefficients 
of correlation from the points where the curve crosses the ordinates at the 
various abscissae very nearly equals zero, so that the curve is not entirely 
arbitrary. 



92 



Educational Guidance 



Yr. in 

Question 





1 Yr. Be- 

PORE 
1 



2 Yrs. Be- 
fore 
2 



3 Yrs. Be- 
fore 
3 



Yrs. Be- 
fore 
4 



1 

2 
3 

4 
<r's 



.67 
.58 
.53 
.50 

<T0 



.67 
.58 
.53 

0"! 



.67 

.58 

0~2 



.67 

0~3 



The following regression equation is derived from the table: 

X = . 4616 -° Xi + . 1458 - X 2 + . 0910 - X 3 + . 1098 - X* 

a\ 0"2 °"3 0"4 

In case the standard deviations are all equal, this equation becomes, to a very 
close approximation: 54.9 X = 25Xi +8X2+5X3+6X4. 



Teachers' Estimates and Combinations of the Same 

Having the estimates of several teachers of the mental traits of each pupil, 
it is necessary to combine these estimates into single measures of the trait in 
question for the pupil in question. Each teacher reported on about 25 pupils, 
and it is assumed that the talent follows a normal distribution. The rankings 
of the teachers were then expressed as deviations from their respective means, 
using the same method as used in transforming literal into numerical grades. 
The number of gradings obtained for each pupil ranges from two to seven. 
It will be seen from the following table that the correlation between these 
estimates is low: 

r (i. a. —first judge) (i.a.— second judge) — ' ° ■*-'" 



"(cons. " 


) (cons. 


\ — .oort.uz^ 


'"(emo. int. " 


) (emo. int. " 


) = .31±.024 


r (exp. 


) (exp. 


) = .29±.024 



Because of this, it is impossible to average these grades and have them even 
approximately comparable, for the standard deviation of the measures which 
are the averages of the grades of two judges is materially greater than the 
standard deviation of the measures which are the averages of the grades of a 
greater number of judges. The extent of this difference can be readily esti- 
mated, for if Xi, X% • • • X n are measures of the same trait, and if r is equal 
to the correlation between such measures, and if sigma X x = sigma Xj 
= • • • sigma X n , then we have: 



z + 2X 1 X2+Xf) 



fr-kr-%/* Cyi+X ° , -l/ gg * 

-v/ 2m+ 4 a r^ -w^ 



Appendix 



93 



Similarly, 



Finally, 



°Xi+X2+X ; 



°Xi+X2+ ■■• x. 






+2r 



+ (n-l)r 



In order to make the standard deviations of measures which are averages of 
varying numbers of estimates comparable, it is only necessary to divide the 
measures by their respective sigmas, i.e., if but a single measure divide by sigma 

v I y 

Xi) if an average of two measures divide by sigma — k — , etc. The follow- 
ing table gives the desired divisors for the various cases: 1 



No. of grades 


I. a. 


Cons. 


Emo. i. 


Exp. 


averaged 


Intellectual 


Conscientious- 


Emotional 


Expression 




ability 


ness 


interest 




1 


.92 


.92 


.92 


.95 


2 


.74 


.79 


.74 


.76 


3 


.66 


.73 


.66 


.68 


4 


.63 


.69 


.63 


.65 


5 


.61 


.67 


.61 


.63 


6 


.59 


.66 


.59 


.61 


7 


.58 


.65 


.58 


.60 



The mean number of grades averaged to obtain each individual's measure is 
about two and one-half, therefore the reliability coefficients have approxi- 
mately the following values: 

r (i.a. measures as derived) (i. a. meas. similarly derived) = -493 
r (cons. " " ) (cons. " " " ) — -605 

^(emo.i. " " ) (emo. i. " " " )=.505 

J"(exp. " " ) (exp. " " " )=.529 

In 23 cases of group 2, teachers' estimates were not available, except teachers 
of English and history who later had the same pupils in test courses, which were 
continuation courses of the first half year's work under the same teacher. 
The estimates of such teachers were not used when it could be avoided, i.e., in 
all cases except these 23. The following correlations justify excluding such 
estimates: 

r G(i. a. — estimate of geometry teachers) ** "*V I P°P* = "' 



r G(i.a.- 

r E(i. a.— 
r E(i. a.— 



other 

English 
other 



j = . 44 \ group 1 

) = .54/pop.=33 
x = .36 I group 2 



1 This method of averaging varying numbers of correlated measures was 
used frequently in other portions of this study, e.g., in averaging grades of 
pupils for some given term or year where the number of studies varied 
appreciably. 



94 Educational Guidance 

The estimates of "other" teachers may be considered as accurate as those of 
the geometry or English teachers, so that the excess of .57 over .44, and of .54 
over .36 is, in a sense, a measure of the extent to which a teacher's estimate is 
based upon the unique ability shown in the subject he teaches. 

The combination of the measures, based upon teachers' estimates, into a 
single final measure or estimate of scholastic ability is accomplished by the 
usual regression equation, as follows: 

Av. I. a. Cons. Emo. i. Exp. 
La. .72 
Cons. .62 .61 

Emo. i. .58 .61 .66 

Exp. .63 .82 .55 .59 

<f'b 4.048 5.193 5.166 5.138 5.190 

Av. = . 3584 14|? (I. a.) + . 2456 1^ (Cons.) + . 1161 §-|§ (Emo. i.) 
Z. 591 o.ooU o.o4/ 

+ Q471 2J530 (E j 

2.905 

or Av.= .364(1. a.) + .183 (Cons.) + .086 (Emo. i.) + .043 (Exp.) 

or, approximately, 1.1 (Av.) = .4 (La.) + .2 (Cons.) + .l (Emo. i.)+.05 (Exp.) 

— which is a very simple equation to use. 

r (Av.) (I. a., Cons., Emo. i., Exp.) = ■ 7551 - 



Bearing of the Various Factors, I. a., Cons., Emo. i., and Exp., upon M, E, 

and H. 

From the accompanying data: 
M t .e. = -460^-La. + .114-^L M j & Cong . Emo . j. Exp . 



La. "Cons 

Cons. +.129 



La. .591 



Emo. i. 



Emo. i. .472 .61 .66 
Exp. .496 .82 .55 .59 
^M - o-'s 



-.014— *- Exp. 8 M "La. "Cons. " Emo. i. "Exp. 



a 



Exp. 
r MM =.61 (Population = 178). 

From the accompanying data: 
a 



E t =.336— 1- 1, a. +.261 — — _ T ~ „ . „ 

*■ e - (T T CT Pnnq E I. a. Cons. Emo. i. Exp. 



'La. "Cons. 



La. .598 



Cons.+.OeS-^-Emo.i. g ons - . -Jg .61 

a v „ ; Emo. i. .487 .61 .66 

hm0 - 1 - Exp. .536 .82 .55 .59 

+.083-^- Exp. <r ' S °" E °" La - ^Cons. °Emo.i. °Exp. 
°"Exp. 
r EE =.64 (Population = 179) 



Appendix 95 

From the accompanying data: 



a 



H fce# = .450— 5-1. a. -.024. 



Oj a <r c H I. a. Cons. Emo. i. Exp. 

0n8 ' I. a. .381 

Con B . + .30 5 ^_ Em o.i. Con,-..™ .6. 

Em01 - Exp. .245 .82 .55 .59 

-.287 -fl- Exp ^ °" H °"l.a. ^Cons. ^Emo.i. ^Ezp. 

^Exp. 
r HH{e = .46 (Population = 68) 



Grading op the Algebra Test 

Having the gradings for the various problems in the algebra test, it is 
impossible to say, a priori, with any assurance, which are the most significant 
and which are the least so. The common procedure in a case like this is to call 
them all of equal importance and add or average. Whether such a procedure 
results in getting out of the data all that is in them or not, is a fit subject for in- 
vestigation. The question is simply this — does the magnitude (grade of prob. 
1 + grade of prob. 2 • • • + grade of prob. 14) correllate as highly with the 
algebra grade received at the end of the school year, as the magnitude (Ci X grade 

of prob. l+C 2 Xgrade of prob. 2-\ C u Xgrade of prob. 14) where &, C% • • • 

Cu have the best values possible. Of course the second magnitude would result 
in the higher correlation, or, what amounts to the same thing, the stand- 
ard deviation of the residuals in the second case is smaller than the standard 
deviation of the residuals in the former case. Using the notation given by 
Yule, this is to say that 

°A. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 < °A. 1+2+3+4+5+6+7+8+9+10+11+12+13+14 

(A = grade in algebra course, 1 = grade of first problem, etc.) It is manifestly 
impractical to attempt to calculate °a l 2 3 4 5 6 7 8 9 10 ll 12 13 14 Du ^ an 
approximation to this may be obtained if the problems 1, 2, • • • 14 that have 
about the same standard deviations, and that are correlated to about the same 
extent with A, and are correlated with each other to approximately an equal 
extent, are grouped, thus reducing the variables to such a number that the 
calculation is feasible. In attempting to fulfill these conditions, problems 1-4, 
8-11, were grouped, as were also problems 6, 13, 14, giving groups A', B', C, 
respectively. The question then is to determine <r A &> B' C anc ^ ° A A'+B'+c* 
Formulae giving these expressions (derived in the next section) are as follows: 

a _ 2 H Sr \ A> - Wr AA ,r AB ,r A , B ,- Hr^r^, +2i:r AA ,r^ / r A , c ,r i? , c ,~] 

L 1 -^ r2 A'B'+ 2r A'B' r A'C' r B'C J 



°A. A+B'+C 



,= <r t 



j _ i^AA^A') 



*o\, + 2?,t a , bi o- a ,o- e 



96 



Educational Guidance 





A 


A' 


£' 


A' 


.39 






B' 


.41 


.17 




C 


:39 


.41 


.42 


c's Estimated 




10.3 


7.0 


From which 




2 2 
0" A. A'B'C = . 705 cr A' 





The various coefficients of correlation and standard deviations required, are 
given in the following table: 



7.0 



a A. A'+B'+C=. 711 <r A . 

These coefficients were calculated by the per cent of unlike signs method 
and only approximate to Pearson coefficients of correlation, which are necessary 
from the theoretical standpoint, but it is thought that they satisfactorily serve 
the purpose of this preliminary investigation. 

The difference between the standard deviations given above is so small 
that the advantage of the regression method over the simple average or sum 
method is plainly too slight to justify the added work, and the measure for the 
algebra test is taken simply as the sum of the grades in the test, after subtract- 
ing the mean and dividing, for convenience, by 5. 



That is, 



At 



A'+B'+C'-me&n 



Here, as in the case with all measures used in regression equations, At is a 
deviation from the mean. 



Derivation of Formulae 



a\.2=a\(l-rh 2 ) 
<T\.n= o- 2 i(l-r 2 i 2 )(l-r 2 xs. 2 ) 

r 2 12 4-r 2 i3— 2r 12 ri 3 r 2 3 



= <T'l 



or = a\ 



1- 



1- 



l-r 2 23 
Sr 2 12 — 2Sri 2 ri 3 7-2; 



Formula for 2 variables. 



Formula for 3 variables. 



1-Sr 2 23 

.-rWCl-rW 

l—r 2 i3-2—r 2 u.ir\ i .2+2 ^3.2^4.^34.2 
= o" 2 1 (l-r 2 i 2 ) ( 1 



-*[i- 



l-r 2 34.2 

Sr 2 i 2 -2 Zrururn— Sr 2 i 2 r 2 34 +2 Sr^r^^^ 
l-Sr 2 23+2r-23r 2 4r34 



Formula for 
4 variables. 



Appendix 97 

where 2r n rur 2 3 ^TiffittPu+rvSriffiH+ruPifu 2r 2 J2 =r 2 i 2 +^13+^14 
Sr 2 i 2 r 2 34=r 2 i2r 2 34+r 2 i 3 r 2 24+? ,2 i4r 2 23 
Sri 2 ri3r 2 4r34 = ?"i2r , i3r24» - 34 +ri2r-i 4 r23r 3 4+ri3ri4r23''24 
2r 2 23=r 2 23+r 2 24+r 2 , 4 



= <r 2 (1-rt + ) = o- 2 [~1 - (ri2q " l0 " 2+ri3q " l0 " 3)2 "1 
1 [_ <r 2 i (cr 2 2 + ff 2 3 -\-2r2zG2G1) J 

_ 2 T (ri 2 q- 2 + ri3q-3) 2 1 

O- 2 2 + O- 2 3+2r230W3j 



Similarly, 

o\ .2+3+4 

(Sri2(r 2 ) 2 



_ 2 I (Vi2(72+ri30-3+ri4(r4) 2 "1 

1 [_ o" 2 2+(r 2 3+o- 2 4+2(r23a20-3+r24<r 2 <r4+r34(r3o-4) J 

= ff 2 i|~l- 



S<T 2 2+2Sr 2 30'20'3 

It may be easily shown that this last formula is general and holds good for any 
number of variables. 

It was attempted to derive a formula for OTj 2345 , but paper and patience 
were exhausted before it was accomplished. The law governing the coefficents 
of the terms of the formula for <r l 234 is not sufficiently clear to enable the 
author to state a general formula applicable to residuals of higher order. 

Grading op Geometry Test 

The plan adopted in connection with the algebra test is used in combining 
the parts of the geometry test. The following table of coefficients of correla- 
tion (calculated by per cent of unlike signs method) supplies the necessary 
data: 

G' W 







G 


E' 


F' 


E' 




.25 






F' 




-.06 


.13 




G' 




.22 


.19 


.06 


H' 




.40 


.13 


.09 


Estimated 


a's 




3.3 


7.4 



.45 
4.0 9.0 

E'=problem 1; F' = problems 2, 4, 5, 6; G' = problem 7; #' = problems 8, 9, 10. 
Problem 3 turned out to be too easy for the group in question, some 98 per cent 
making a perfect score, so its grading is not used. The surprise in this table is 
the small negative correlation between G and F'. Because of this small 
correlation F' is also discarded. For the balance of the data the advantage of 
the regression method over the average method is negligible, as the following 
standard deviations show: 

ff2 G. E'G'H' =-800o- 2 G <*G. E'G'H' =.894(T G 

^G. E'+G'+H' = -817o- 2 G a G. E'+G'+H' =- 904 O"G 

°G. E'+F'+G'+E' = ■ 925 °G 

Accordignly the sole measure of the geometry test is taken as the average of 

W. O; W; =i.e. G, £ ' +G ' + «'- meaD - 



98 Educational Guidance 

Grading of the English Test 

The following gradings of the English and history tests may be of particular 
significance as evidence of ability in English: E a (accuracy of description in 
the English test), E v (valuation of important factors in. the English test), 
W (written expression in both English and history tests), D (dramatization in 
both English and history tests). 

The correlations between dramatization and English and history were cal- 
culated by the percentage of unlike signs method, to determine with which of 
these subjects dramatization is most closely associated, with the result that 
'ED = "40 a t er calculation gave Pearson coefficient of correlation to equal .182) 
and r HD = .09. The correlations between English and the other elements, men- 
tioned above, are as follows: r EE =.64, r EE =.59, r EW = .56, when calculated 

by the unlike signs method. (Later calculations show that these are somewhat 
larger than the Pearson method would give.) Furthermore, the correlation 
between written expression and dramatization is .61 (by the unlike signs 
method). The grading for dramatization is seen to be more closely related 
to English than history, but because of its high correlation with written expres- 
sion it contributes little that is unique, even with reference to English and is, 
accordingly, not evaluated with respect to either English or history. 

Another factor in connection with dramatization is the question of whether 
its relation to English or history is linear. In grading the papers, the author 
was quite impressed with the feeling that high grades in dramatization were 
more likely to accompany good or poor grades in English than medium grades. 
The author was totally unaware of the English grades of the pupils at the time 
of the grading for dramatization, so there was no reliable foundation for the 
belief . After the grades were available this question was tested by inspection 
of the regression line in the correlation table for English and dramatization 
and by calculation of the correlation ratio. The regression fine was irregular, 
but did show some evidence of such non-rectilinearity. The value of the 
correlation ratio between English and dramatization is .241. (Compare with 
r ED = .182.) The excess of .241 over .182 is not sufficient to warrant the 
assertion that the regression is not rectilinear, according to the criterion estab- 
lished by Blakeman, 1 but the chances are in favor of its being non-rectilinear, 
so the question is still an open one. 

To return to the determination of the method of combining the parts of the 
English test: the following table of coefficients of correlation (unlike signs 
method) gives the necessary data: 

E E a E v W 

^E.E a E v W =^E,69 |a .64 ^ 

°"E. Ea+Ey+w-^E^i w .56 .75 .64 

Estimated o-'s 2.5 2.2 1.65 

The advantage of the regression equation method is so small as not to justify 
the added labor necessitated by its use, and the simple average, for convenience 
multiplied by 2, of E a , E v and W, is taken as the measure in the English test. 
That is, E t = f(E a -t-E v +W-mean). 

1 See J. Blakeman, Biometrika Vol. 4, pp. 349-50, for criterion of recti- 
linearity: Here the function of -q and r in question = 1.69, which is less than 
2.5 the required value if non-rectilinearity is to be definitely established. 



Appendix 99 

Gbading op Histoky Test 

The population in the case of history is small and therefore Pearson coeffi- 
cients of correlation were calculated for the preliminary investigation, instead 
of the less accurate coefficients calculated by the percentage of unlike signs 
method. The data are as follows: 



<r 2 H.H a H v =-898<r 2 H . H H a H v 





H 


H a 


H a 


.31 




H v 


.23 


.62 


<r's 




2.40 



* 2 H.H a =904 <r' H . ff , a 24Q 16Q 

7- HH =V.096 = .310, and similarly we may say that the total correlation 

between history and the c ombi ned measures H a , H v is given by the following 
expressions: r- R , H , H ^V. 094 = .307 and r H(H H \=V. 102 = .319, where the 

notation r-a iv , „ N is understood to mean the correlation between historv and 
u cn a n v ) 

H a and H v when combined into a single measure by the regression equation. 

The above results show that the average, or sum, H a +H v , will give a lower 

correlation than H a alone, and that the regression equation yields but .009 

higher correlation. For these reasons the sole measure of the history test is 

taken to be H a , for convenience multiplied by two. That is, Ht = 2 (H a — mean) . 

Bearing op the Various Tests Upon Mathematics 

(a) Algebra. 

To evaluate the significance of the algebra, English and history tests in 
their bearing upon algebra, the regression equation between these tests and 
algebra grades may be calculated. The following table gives the required data : 

A A test E test H test 
<r 2 A.A t E t H t =-728o* A At .47 

ff A.A t +B t +H t -- //b<r A Ht .27 .27 .40 

<r's 4.977 3.856 3.286 5.460 

There is here a material advantage to be gained by the use of the regression 
method, and it has accordingly been calculated: 

Act = 1.316(A) = .6(At)+.4(E t )+.ll(H t ) 

(b) Geometry. 

A procedure, similar to the above for algebra, gives the following results: 

G Gt Et Ht 

* 2 G.G t E t H t =.820o* G Gt .42 

„•> _ c* fi/T 2 Et .24 .42 

a G. G t +E t +H t --^ b<7 G Ht .21 .20 .40 

o-'s 5.010 3.751 3.042 5.176 

Get = 1.53(G) = .8(Gt) + .08(Et) + .183(Ht) or Get =.8[(Gt) + .l(Et) + .23(Ht)] 

The constant 1 .53 has been so chosen that the standard deviation of G c t is 
very nearly equal to the standard deviation of A c t- This is needed, for later A c t 
and Get measures are used in the same calculation and called M c t measures. 



100 Educational Guidance 

Bearing op the Various Tests Upon English 

In the following tables which give the data for the calculation of the regres- 
sion equations for English with the (1) algebra, English and history tests, 
and (2) geometry, English and history tests, the probable errors of the calcula- 
tion involving the algebra and geometry tests are given: 

Since the following coefficients 
of correlation ± their respective E At Et Ht 

probable errors overlap, 
*EA t and r Wt ; 

r E t A t and r E t G t ; 
r HtAt andr HtGt ; 

and since the standard devia- 
tions of At and Gt ± their prob- E Gt Et Ht 
able errors overlap, At and Gt 
may be combined into a single 
mathematics group, Mt, without 

materially affecting the regres- o"'s 3. 860 ±.298 3.274 5.440 

sion equation. 

The regression equation has, accordingly, been calculated from the follow- 
ing table, in which the coefficients of correlation involving the algebra test 
and geometry test are weighted averages of the coefficients for the algebra and 
geometry tests separately: 

From this table are obtained e Mt Et Ht 

the following standard devia- 
tions : 





E 




At Et 


At 
Et 
Ht 
c's 


.35± 

.44 

.40 


05 


.37±.05 
.27±.06 .40 
3.917±.239 3.274 




E 




Gt Et 


Gt 
Et 
Ht 
<r's 


.31± 

.44 

.40 


07 


.42±.07 
.20±.08 .40 
3.860±.29S 3.274 





E 


Mt 


Et 


Mt 


.34 






Et 


.44 


.38 




Ht 


.40 


.25 


.40 


(T'S 


5.254 


3.896 


3.274 



°" 2 E. MtE t H t = • 722 °" 2 E 

* 2 E.M t+ E t+ H t - 729 ' ? E 5254 3896 3274 544 ° 

There is so little difference between these standard deviations that the 

^ 3 • j • ^ Mt+Et+Ht . . . . . _, 
simpler method is used, i.e. E = > designated by E c t. 



Bearing op the Various Tests Upon History 

By parity of reasoning, the same English combination measure, E c t, is used 
to correlate with history. The data bearing upon the problem are as follows: 

ff2 H. MtEtHt = -787(7^ 
* 2 H. [Mt+Et+Ht =-793^ H 

From which it may be deduced 1 that r } 

calculation Appx. p. 105, but care should be exercised in using values obtained 
in this way as it should be noticed that errors are cumulative and an error 
introduced here by throwing away .001's, or for other reasons, may affect a 
subsequent correlation considerably.) 

1 Same method used as in paragraph upon Grading of History Test, Appx. 
p. 99. 



H 


Mt 


Et 


Ht 


Mt .37 
Et .35 
Ht .31 
o-'s 5.156 


.38 

.25 

3.890 


.40 
3.136 


4.796 


bat rTiTT =.455. 
HH ct 


(This 


value is 


used in the 



Appendix 



101 



Interest Tests — Grading of Books 

In expressing the grades of the books 1, 2, . . . .7 for English, as deviations 
from the mean, a normal distribution was assumed for the grades given by each 
of the judges — this method seemed to be necessary as the means for the different 
judges varied appreciably — and use was made of the same kind of a transforma- 
tion as in expressing literal grades in numerical terms. 

In the case of the history grading, it does not seem reasonable to assume a 

normal distribution, as a straight history is surely a greater distance above the 

mean, as evidence of interest in history, than is a book like "Kite Flying for 

Boys" below the mean. No simple method is at hand to tell the nature of the 

distribution of the books with reference to their historical significance, but the 

assumption of a skewed distribution of some sort is surely more reasonable 

than the assumption of a normal distribution. A distribution skewed .75 was 

, r , 3 (Av.-Median) t 
assumed, skewness being measured bv the formula With 

a distribution so skewed, grades 1, 2. . . .7 were expressed as deviations from 
the mean in the same manner as was done for the grading of books for English, 
and for literal grades, under the assumption of a normal distribution. 

It may be mentioned that the calculation of the reliability coefficient for the 
grading of books foi history was done before the above-mentioned transforma- 
tion was made, so that a small inaccurac} r is present. Calculation of this 
coefficient after the transformation would raise its value a little above the 
obtained value, .720. 

In grading sports, entertainments, words and magazines, it is not necessary 
to resort to a transformation, for even though the means should be quite differ- 
ent for different judges, a simple average may be taken, for the standard devia- 
tions of the grading of the different judges were found to be very nearly equal, 
and every judge graded every item except in the case of magazines, where the 
means, as well as the standard deviations, were nearly equal. This does not 
introduce the error that would have resulted from such a procedure in the case 
of books, where the books that were graded by only two judges were not, in 
many cases, graded by the same two. 

Grading of the Interest Tests with Reference to (a) English, (b) 
Mathematics and (c) History 

The data in the following table serve as a basis for combining the various 
parts of the interest test into a single measure to correlate with English. 

Bks. 

Sports 

Entertainments 

Vocations 

Factor of accuracy 

Words 

Magazines 

Books 

o-'s 1.965 3.512 2.059 4.286 4.161 2.232 2.428 



E 


Spts. 


Ents. 


Vocs. 


F.ofA. 


Wds. 


Mags. 


.20 














.14 


.5 












.24 


.3 


.1 










.04 


.2 


.1 


.1 








.26 


.3 


.0 


.1 


.7 






.37 


.4 


.3 


.4 


.2 


2 




.13 


.3 


.0 


.2 


.0 


^3 


.3 




1.965 


3.512 


2.059 


4.286 


4.161 


2.232 



1 The actual distribution used is that represented in Thorndike, Mental 
and Social Measurements, Ed. 2, p. 74, but any reasonable distribution with a 
skewness of .75 would yield comparable results. 



102 



Educational Guidance 



The coefficients of correlation in this table which involve English were calcu- 
lated by the Pearson formula, and the balance by the percentage of unlike 
signs method. 

The standard deviations given in this table are not the standard deviations 
of the original measures. Certain of the measures were grouped for con- 
venience in handling: The following relations hold between the above stand- 
ard deviations and the standard deviations of the original measures: 

1 . 965 = Standard deviation of original grading of sports. 

3.512= entertainments. 

2.059= " " " " vocations. 

4.286 = 20 " " " " factor of accuracy. 

4.161= .2 " " " " words. 

2.232 = 3.3 " " " " magazines. 

2.428 = 3.3 " " " " books. 



The labor involved makes it plainly out of the question to calculate a regular 
regression equation, so that a rough approximation only has been attempted. 
Since the grading of the magazines correlates the most highly with English, 
the effect of that one factor is taken into account by calculating partial coeffi- 
cients of correlation of the type r E gpts . Mags , r EEnt3 . Mags , etc. All such par- 
tial coefficients of correlation are given in the accompanying table except 
r E F of A ■ Mags - '^ ne f a °tor of accuracy is very highly correlated with the 
grading of the words, and is therefore evaluated in connection with it. 



r E F of A ■ Wds • 206 


r E Spts 


• Mags — 


.061 


r B Wds • F of A = • 325 


r E Ents 


Mags — 


.033 


Probably the average of r E Wds . Maga 


r E Vocs 


Mags — 


.108 


and ns Wds • F of A gives a better weight 


r EWds 


Mags — 


.204 


than either alone. 


r EBks 


Mags — 


.021 



This gives .265 as the weighting for Wds. and proportionately —.168 for 
Fof A. 

The weight assigned to magazines is the average of the following partial 
coefficients of correlation: 

r E Mags • Spts = - 331 
r E Mags • Ents = ■ 348 
r E Mags- Vocs = - 308 
r E Mags • Wds = • 336 
r E Mags • Bks = • 350 

average = . 338 



Having weighted Mags .338, proportionate weightings for other variables are 
as follows: 

.338 X 



.331 .061 
Similarly 



, X = weighting for Spts. = . 062 

"Ents. = .032 

"Vocs. = .119 

" "Bks. =.020 



Appendix 103 

Since Spts. and Ents. are highly correlated, the weights assigned to them above 
are somewhat too high. A small amount is arbitrarily deducted from the 
above weights. The final weights assigned are as follows: 





W'ts 


Spts 


.058 


Ents 


.026 


Vocs 


.119 


Fof A 


-.168 


Wds 


.265 


Mags 


.338 


Bks 


.020 



These weights, divided by the respective standard deviations, give the multi- 
pliers of the various measures used to obtain a single interest and information 
test grade. The single grade for the interest and information test in its bear- 
ing on English (Ei) is accordingly given by the following equation: (In the 
following equation the letter E indicates that the grade assigned is in relation 
to English.) 

. 1515 Ei = . 0295 (Espts) + . 0074(EEnte) + . 0578 (Evocs) - . 0392(F of A) 
+ . 0637 (Ewds) + . 1515 (EMags) + . 0082 (EBks) 

( . 1515 is taken for convenience, to make the coefficient of EMags equal to 
unity.) 

.-. Ei = . 195 (Espts) + . 048(EEnts) + . 382(Evocs) . 259 - (F of A) + . 420(Ewds) 
+1.00 (EMags) + .054 (EBks), or, for practical purposes, 

Ei = . 2 (Espts) + . 0£ (EEnts) + . 4](EVocs) - . 2§ (F of A) + . 4 (Ewds) + 1.0 (EMags) 
+ .0^(EBks) 

The same relative weighting is assumed in obtaining a single measure of the 
interest and information test to correlate with history (H) and with mathe- 
matics (M), except that the F of A is weighted differently, since r H F of A = .094 
and r MFof A = .173. The following weighting is used. 

Hi = . 2 (Hspts) + . 0| (HEnts) + . 4 (Hvocs) - . 1 (F of A) + . 4 (Hwds) 
+ 1.0(HMags) + .0KHBks) 

Mi=2[.2(Ms P ts) + .0MMEnts) + .4(Mvocs) + .0|(Fof A) + .4(Mwds)] 

The factor 2 in this last equation is simply for the purpose of obtaining a 
more convenient distribution — by maintaining distributions with 20 or more 
divisions it is not necessary to correct for grouping or for arbitrary means. 

Combination op Parts of Interest Test Mi, Ei, Hi, with Reference 
to (a) Mathematics, (b) English, (c) History 

(a) Mathematics. 

Although the interest test has been graded specifically with reference to 
mathematics, it may be that the gradings with reference to English and history 
give some light upon the most probable mathematical standing of the pupil. 



104 Educational Guidance 

The calculation of the regression equation involving M, M;, Ei, and Hi will 
decide the question. The data for this calculation follow: 

From this o- 2 MM . E . H .= . 91 1(7 2 M , M Mi Ei Hi 

from which it may be deduced that 



6.12 





M 


Mi 


Ei 


Mi 


.24 






Ei 


.20 


.21 




Hi 


.15 


.54 


.63 


<r's 


4.93 


4.64 


3.13 



'MCMiEiH;) - • 298 

This correlation is considerably above 

the correlation for r MM ., which equals 

. 24, and by inspection of the table, it is apparent that it is considerably above 
r M(M+E-+B»> f° r tne l ar § e standard deviation for history (6.12), operates, when 
taking an average or sum, to weight the history grading the highest, so the 
regression equation method is plainly the method needed. Calculation gives 
the following: 

4.701 4.701 4.701 

M= - 2238 3^35 Mi + 1826 2li0" Ei -° 95 3^5 Hi 
= .2822 Mi+.3669 Ei-.1120Hi 

Multiplying by the convenient factor, .5646, and designating the result by M c i 
(combination of the parts of the interest test with reference to mathematics) 
gives the following: 

M c i= .500Mi+.650Ei-.199 Hi, or for practical purposes, Mci =.5 Mi 
+ .65Ei-.2 Hi. 

(6) English. 

Similar data with reference to English are: 
From this E Mi Ei Hi 

* 2 E.M iEi Hr- 7830r2 E Mi 

from which it may be deduced that J. 

r E(M i E i H i )=.464, o-'g 5.23 4.64 3.13 6.12 

but as r^. = . 46 there is practically no object in using the longer method. 
Ej is therefore taken as the sole measure of the interest test in its bearing upon 
English, and for such use will be designated E ci . 

(c) History. 

The data referring to history are as follows: 

From this . H Mi Ei Hi 

^.MiEiH^- 875 ^ 
from which it may be deduced that 

r H(MiEiHi) = . 353 <7's 5.10 4.64 3.13 6.12 

It is evident that r H(M +E+H-) ^ appreciably lower than this, for the rather 

large standard deviation for Mi (4.64) would operate to weight Mi quite 
heavily. The correlation .353 is sufficiently higher than the correlation rgg. 

(.30), to make the regression equation desirable. By calculation, 

4.891 4.891 4.891 

H= - 1597 3r^i Mi+0767 2T^ Ei+ - 2319 3Ti5I Hi 

= - . 2070 Mi+ . 1585 Ei+ . 2910 Hi 



E 


Mi Ei 


.15 




.46 


.21 


.32 


.54 .63 


5.23 


4.64 3.13 





H 


Mi 


Ei 


Mi 


.02 






Ei 


.27 


.21 




Hi 


.30 


.54 


.63 


o-'s 


5.10 


4.64 


3.13 



Appendix 105 

To obtain a convenient distribution and a simpler equation to work with, 
this equation has been multiplied by 2.406. The result is designated by H c j. 
H c i = -.498 Mi +.381 Ei+.700 Hi, or for all practical purposes, H c i= -.5 Mi 

+ .38Ei + .7Hi. 

Combination of the Mathematics Tests, M c t and M c i, with Reference 
to Mathematics. Similar Combinations of English and History 

Tests 
(a) Mathematics. 

On page 99 of the Appendix, mathematics, English and history tests, Mt, Et, 
Ht, were combined into a single grading, M c t, which gives the total bearing of 
these tests upon mathematics. On page 104 of the Appendix, the gradings of 
the mathematics, English and history interest tests, Mi, Ei, Hi, are combined 
into a single grade, M c i, which gives the total bearing of the three interest 
tests upon mathematics. It now remains to combine M c t and M c i into the 
single measure which correlates the highest with M. This single measure will 
be designated by M c , and is given by the following regression equation, which is 
based upon the accompanying data: 

4 » 4 co M Mci Met 

M = . 1606f^ Mci +.4198^5 Met M ci .30 

• 4.VOS Tyj aq QC 

Multiplying by the convenient factor _,„ KO o ■t'o'a o aq 

1.556 gives: a B 5 ' 23 186 348 

M c = . 658 Mci + 1 . 00 Met, or, for practical purposes, 
M c =.66 Mci + Met. 

This relative weighting is used whether it is desired to combine the grades 
of the tests with reference to algebra or geometry. If the derivation of regres- 
sion equations for algebra and geometry had been undertaken separately, the 
difference from the above weighting would have been slight and the increased 
correlation due to the more exact weighting would have been inappreciable. 
The terms A c and G c will be used instead of M c , when it is desired to speak 
of the algebra combination, and the geometry combination, rather than the 
mathematics combination. 

(h) English. 

Data for English, similar to the above for mathematics, are given in the 
accompanying table: 

E Eci Ect 

Eci .46 

Ect .46 .34 

o-'s 5.23 3.21 3.23 

Since r EE . =?" EE , and ff E . is very nearly equal to <r E , a straight average or 

CI ot CI ct 

sum of the two measures is the desired combination, i.e., E c =E c i+E c t. 

(c) History. 

The data for history are given in the accompanying table: 

Calculation gives: H Hci Hot 

H - oiw 4 - 446 n-4- o7,oo 4446 H, H « -33 

H ~- 2154 4^20 Hci+ - 3782 2~813 Hct Het .45 .33 

= . 2168 H c i+ .5979 Hct *'« 5.10 4.80 3.23 



106 Educational Guidance 

Multiplying by the convenient factor, 1.673, and designating the result by 
H c , gives: 

H e = .1814 Hci+1.00 H c t, or, approximately, H c =.2H c i+H c t. 

Combination of Elementary School Standing, Teachers' Estimates 
and Test Standing with Reference to Average Class Standing 

The estimation of average class F A 7,6,5,4 A Est A T A 

standing based upon all three 7 ( 6, 5, 4 A . 83 
sources of data is by means of the EstA 81 68 

following regression equation, based 
upon the accompanying data: TA -51 .56 .54 

.4458 0V .4458°V 

F A= - 6422 ^Zn^ " < 7 ' 6 ' 5 ' 4 A ) + .5983 A Est A 

. 5340 o"(7, 6, 5, 4 A ) . 5666 (7 Est 

.44580V ^ 

-.0771 -i T A. 

.79730-t 

The equation is left in this form for reference to it. The values of the various 
standard deviations are: 

<t Fa =3.662; <r (7i 6i 5> ^ = 4.665; ^ = 6.660; ^=3.845. 



SECTION 12 
GRADE AND TEST DATA 



108 



Educational Guidance 



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rHCNC0^U3«Ot-00C»©'-ICNCO'<l<lOCDt»00O5©i-l 



Appendix 109 



<Ht»t^aoioi-toc»to<o©»o!^*Ht»a5cq,*eqc5'«j<Ni_,iH«oro^<ooi-<©c<!coc5«eqcO'*,f 



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cn ■* 10 r-« a> co co •-< e» -4 © 1-1 »-i 1-1 cn» cn co •* co o —1 c* •& <-< © -h o in co in *nt» ^.-icocn 
III I I I I I I I I III I I I I I I 

r» m 11 o 1-1 — 1 « c« as © eo eo © i-t ■* » co «3 1» n in ih ifl i-i co rn os 50 co >h cooo o^cot- 

III III I ~ I I II I III MM I I H "I 



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II I If I f II II I f I If 

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i^MCOCN00«rtcO>OCOT»lU5TlltNCO©COtNiO©i«CN>O'*X©(N>OININ00»-l©COlOtN©lO 
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NO»OTjiN©CN©©©®b-NINNcO'*S»roiNrt-*Tj<cN»<N«©©CO©'<*cNlO©INlN 

f I I Mill II l-l^ I 

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if 1 1 1 1 11 1 in 1 i rt 1 1 

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+ ++ + + ++ + 
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+ +++ + ++ + +++ + 1 

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1 + +1 +++ + + 1 

OPOO OPfflOQ PO QB Ofl O ° OW 0° O 

+ + +I ++ ++ +1 

opmo opmop o« o< op oo p om qq 

+ + 1 + + 

<!«!m«! o t) p o o m oompw 

+ + + + +++ + + + ++ +++ + + + 

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+ ++ + + + + 

op<<m<5m m wppo<i<!ffl<i!«pHppopqo<jpflOw mo m«iop 

+ + + 

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+ X +l 

+++++ ++ ++ ++ I I++ + + + 

oPmm<*mpmmwopmmmm«ipmmpopmpmoopmomo«<mopp 

++ 1 +++++ + + 

op<!m^pwmppppo^mo<jmwpppoop<popm mp omp 



«COTjliCCOt^(>005©iHcNCOT^incOt^l»05©'^iNM^^O^OOO>0'-lcNCO.rt<"5tOt~QOO> 
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110 



Educational Guidance 



a>«DO<NCOi-l.-l©lQOOt--*<M»HIQa>. 






III II I 



r-lTl<.-<e<)©INr-Ct^i-l<N<NT}4Ni-H 

I I III I 



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•i/i pie— H 

+ + ++ I + + 

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++ + + + 

•siv— w ppomooMOwaopmopp 



Appendix 111 



^MOWOMin^t-MMIMiOOlOOiOMIOOlOlOOWCOOOIN 



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I I I l H l I I I II f II II 

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I I M * H M 7 I I t • I 



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112 



Educational Guidance 



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Appendix 113 



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«QO Q OR n Op O O Q O OO U PP<!P« Q O 

+ + ++++ 1+1+1+ +1 +1+ +++ 

M «WW«pOp«««0«!Om POPPO«PPPPpPPOWP«WOPPPPO pOP«P«P« 

+++ + + + ++++ + ++ + + ++ ++ + + +++ + + 

moopp««pp«m«oopoppooppopmppppoo poporaopomopooop o« 
+ + + + ++++++++ + + ++ ++ + + 

«mpQOppQOOOmpq«M«0«OOOOOPQOOOOOOOOOPOOOfflPQPOPO<!0««OPCQP« 

++ ++'++ + + + + + + + + ++++ 

fflMOppwoopmMOM««opp^opompmopoooopo^p<iwppo«oo«o«pmp«i 

+ 
o 

+ ++ ++++ ++ + + + + ++++ 

womop<ooo«<i«iM^o«poom«mo«opp«ooop«op«ffloopm«pooooop«: 

++ ++++++ + + + + +++i + +++ + + ++ 

<ippoo<i;powompo^mPQWooooomp«opQppwwo«wmwwppopw«ooBP3H<ij 



CO^WCOr^OOOSOrtlNMT^iOtOt^OOOSOrtlNCO^iOOt^OOWOrtlNCOTjfiOiOt^OOOSOrtNCOTttintOt^OOOlOrtlN 
COCOCOCOCOMCOT^TfTjlT^^T^^T^T^T^IO^^^OlOlO^OOCOCOCOCOCOCOCOCOCOCOt^t^t^t^t^t^t^^r^t^OOOOOO 



114 



Educational Guidance 



N ^ O 00 CO b- 00 CO 05 t><N tO t- tO ■* CO CO CO to CO 00 t- N N 

IQ iO rfn -^ lO lO t~ ^ >0 1^ O lO CO ^ O lO O O LO lO lO i£> iO tfl 



•H WrH rt | | | | | | S | | ( || 

T„ O»HOMlOlNIMO«5O»-IC*t0NTHrH-*00O'-llN-*INC0i-ie0 

•a i ii iii i i i i i i 

%c\— 4tat iHr-(t0C0'-<©<NC0©C0t0C0(N»0C<l!--lT-IC0©<NC0i-iTi<OC0in 

°~ w II I I I I ~ I I I I I I 



t--* r-tC0>H©lO iH C* U5 ■»)< CO «T)<iH HONHU)^ 

* H i 1 7 1 - 1117 I 

- •*i-l NCOCOT-li-t iHCONOrH ©IOtH BHNMINH 

*a 1 1 1 1 1 1 1 1 

C0t-'<*<C0'*tOT)trHIN«Ji-lr-IC0NC01OC0N>OiHi-IC0C0'tiesi'1< 

io='-w 1 111 1 I I I I I II 



^3 






< 

Q 
H 

W. 



w 1 
Q I 

O g 



I \ s 



* J 



•1 -ocag 
•enoo 



+++ 

I808TK OOMPPO <$0«««Opqtt«0000«PQO« 

+ +i JL + 

•S[v «po<!Opob«pO«00«0<!PO «««ppq« 



I I 



:,+ 



++ ++ 



•wo oonoo a ooQmo pp oowo 
+ + 

+ t + i 

■VBT. OO WOO OMOOMO OO O OWOO 

+ ++t + i 

2n a moom«offlm««m««opqomfflooowmoMO 

+ JL + +++ i.+i,++ JL 

•aioso— H OPO<JOOOMPQOOWOPOPOOOPOOpOOO 

+ + + 

•g MPO«!fflO« «Hpqpq<<fqOMOO«mOpqpqMP«P 

+ + + + + 

■tnoao— -w w o«!OOffl MfflOMOPOPfflOOPWOPpOp 



1 



COT)<mtOl>.00O5©>HlMCO-*mtDt~00C>©'-<C<IM-*iOtDt>00 

ooooooooooooooojososojososoioioicnoooooooo© 

i-HrHrHr-ii-lr-(rHrHi-li-4 r HiHr-lrHrtrtrt(NINC<l<NIMC<l(MC<IC>l 



Appendix 



115 



lOlO!9!0*0!NOOtCW00O(S00l»T(lMNWINe0nOO 



! H 



NN<NCOT»t«Or»eOlOi-HO00C*i-l<NeqTl<(N^<INt-.©N>O<-l 

I I I III III 



13 

is 



< - 
Q 

H 

m 

H 
Q 

w s 
Q s 

tf § 

W CO 
g 

w 
s 

1 

o 



i_ i-ICOe0e<lr-(i-lTl<(NT-<i-l'^<Tj<i-li-t©>-li-l©iOi-l.-l©©©i-l 

•a i i iii ii i iii 

V_ it TAT WNHM(»M(»iONt>OMHHHNMINHTjlMHHWlO 

'-IV ii i i || III I I I I I 



I I I 



I III I I I I I 



1_ 00 lO OS iH CO CO P5 _< C5«5>-lTjt.-liNT»<© 03 i-H 03 P3 i-t 

III, 11,1 , I 

%rr HMWNC5H t(< lO<N<NCO<NN<NtO <-4 CO 00 IN © 

^ II I I I I I I 

'v='*W I III II I II 



■i -oraa 



•!»JV "rood 

otsnj\; 

X 
•ubj^ ptre -^jy 

'H "N P nB 3030 

•jao 

ureiQ 
•duioQ 

a 
•3iv— -jv 



MO 



« O «0«0«PQ«0 



+ + + + +++ 

o«mooMOpq«ooo«««u««oooo««!m<: 
+ ii + ++ 

JL+ + + + + JL++ 

P5<<offlpmo«ooo<)mo<o<jop«ooooo 

+ ++++ ++ + +++ ++++ 

Mmooooo«ffloo«o«««oom««««««< 

i + + + +++ JL + 

o o oop« ooomm «o poo ooo 

i, +++++! +i+ i + + 

OOtQOOPPOOOfflOOfflOOUOQOOOnUO 

J^ + I ]_ +- Lf. JL+ + + + 

QO«ffl«Offl«IOOOOfflOOfflOUqOOOOQD 

+ +JL+++ + + ++JL+ ++ + 

ooomoopMoomoomooooooooomm 

+ + ++ + ++ +i+ ++ + 

oo«oooomoo«oo«oomoo«ooom« 

+ + + 

OOOOQOQ P«P««POPOpP«m«000 

+ + + 

oo«««op<ioo«o«oomffloPMp«M«< 

1 + + JL + + ' + + 

0«fflUOOOfflOBO««OOOOOOfqO««0<! 



•2fe 



CnO'-HINC0'*«O«Dt»0005O— l<NMT)HOtONOOO)OHNM 



116 



Educational Guidance 



HIGH AND ELEMENTARY SCHOOL GRADES 



EXPRESSED AS DEVIATIONS FROM MEAN 



g 


High School 


7th Gr. 






6th Gr. 




5th Gr. 




4th Gr. 


35 


let year 




























fl 


Fm 


Fe 


Fav 


7m 


7b 


7h 


6m 


6e 


6h 


5i 


5b 


5h 


4m 


4b 


4h 
1 
1 


4 


3 


-1 








3 


-1 


1 


1 





1 


2 


1 





-1 


9 


-10 


-10 


-5 


1 


2 





1 


3 


1 


1 


3 


1 





1 


1 


10 


1 


-1 


1 


-2 


-3 





-1 








1 


-1 


1 





4 


-0 


12 


3 


-4 


3 








-1 


-4 





-1 


-3 


-3 


-2 


1 


2 


1 


14 


-4 


-6 


-5 


-2 


3 


2 





7 


1 





6 


4 


-2 


8 


-3 


15 


10 


8 


9 


-3 


-4 


-4 


-2 


-6 


-3 





-3 





-2 


-4 


-2 


16 


-1 


4 


3 


1 


-3 


-2 


2 


-3 





1 


-2 








-3 


—1 


17 


1 


-2 


-2 





1 


1 


2 


3 


2 


1 


3 


1 


1 


3 


3 


18 


-3 


-1 


-2 


1 


2 


1 


3 


5 


2 














2 


-2 


24 


10 


8 


7 





-1 


-3 


-4 


-6 


-2 





-5 


-2 


-4 


-6 


—3 


25 


7 


4 


5 





3 


-3 


-1 


3 


2 


-3 


3 


-2 


-4 


-3 


~3 

- 1 

2 

~0 


29 


7 


4 


5 


-3 


-2 


-2 


-3 


-4 


-2 


-1 


2 





-3 


-4 


36 


3 


4 





-3 


-3 


-2 


-2 


3 


1 





3 


2 


-4 


2 


38 


3 


8 


4 


-2 


-5 


-1 


-3 


-5 





2 


-3 


1 


-2 


-4 


39 


5 





-1 





1 


-2 





3 


-2 


1 


2 


1 


1 


2 


40 


-6 


4 











1 


1 


-1 





-4 


-5 


-1 


-4 


-5 


_1 


41 





-1 


-3 


2 





-1 


1 


-2 








3 


2 


2 





4 


42 


-1 


-10 


-6 


2 


4 





-1 


3 


1 


-3 


2 


1 


-1 


3 


1 


45 


7 


1 


1 


2 


-1 


-1 


-3 





-2 


-3 


-3 


-2 


-4 


-6 


-3 


46 


-4 


-2 


-3 


1 


-1 


1 


-2 


-1 





1 





1 


-2 


1 


-3 


47 


5 


1 


2 





2 





-1 


-1 








3 





-1 


2 


1 


53 


5 


4 


6 


-3 


-3 


-3 


-3 


-3 


-2 


-1 





-2 


-2 


-3 


-3 


65 




-2 





2 





1 


2 


2 


-1 


-1 





1 


3 


2 


1 


76 




-6 


-5 


1 


1 





1 


1 


1 


-3 


-2 


-1 


-1 


3 


1 


89 




-2 


-3 


1 


2 





2 


-3 


1 


3 


-3 


1 


1 





1 


98 




-1 


-2 


2 


3 


2 


4 


2 


2 


1 


3 


3 


5 


5 


4 


103 


-4 


3 


-1 


2 


-1 





1 


-2 


-3 





-2 


-2 


2 


-3 


-1 


106 


-3 


-6 


-3 














1 








-2 


1 


2 


-2 


1 


109 


2 











3 


-1 


-1 


-1 





1 


-2 


1 


-1 


-3 


1 


110 


12 


9 


10 


-1 


-2 


-3 


-3 


-3 


-2 


1 


-6 


-3 


-1 


-5 


-3 


112 


-3 


-2 


-2 


1 


-2 





1 


2 





1 





1 


-3 


-6 


-1 


113 


4 


-2 


1 





6 








5 








6 


2 


2 


2 


1 


116 


4 


-2 


2 





-2 


-1 


1 


-1 





-3 





-2 


-1 


-4 


-1 


123 


3 


-4 


-1 





6 


1 





4 


1 





3 


2 


-3 


-3 


1 


125 


-5 


-4 


-4 


1 


3 








2 


-1 


-3 


1 


-2 


3 


2 


1 


127 





-4 


-2 


-1 


2 








3 


-2 


-3 





-1 


-2 





1 


128 


5 


-2 








2 


-1 


-1 





-1 


-1 








-2 





1 


129 


8 


9 


9 


-1 


-3 


-4 





-5 


-2 


-3 


-6 


-3 


-1 


-4 


-1 


130 


-2 


-2 


-3 





2 





1 


2 





2 


1 


2 


-1 





-2 


135 


-1 


5 


2 


-1 


3 


-1 


1 


2 








-2 


1 


-1 


-1 


-1 


138 


8 


6 


6 


-2 


-1 


-1 


-4 





-4 


-2 


-4 


-2 


-3 


-1 


-1 


143 


6 


7 


7 


-1 


-2 


-2 


-1 


-3 


-3 


-3 


-5 


-3 


-3 


-5 


-3 


145 


2 


5 


3 


-1 


-1 














1 


-5 





-3 


-5 


-1 


147 


6 





3 





3 


-1 





-4 


-1 


-3 


-1 


2 


-2 


-4 


-3 


148 


2 


5 


3 


-2 


-2 


-1 





-1 





-2 


-5 


-2 


-1 


-3 


-1 


151 


5 


-2 


2 





-2 











-1 


-1 


6 


— 1 





2 


-1 


152 





1 


1 


1 


2 














-1 


-4 


_1 


-1 





-1 


153 


-1 


2 


1 


-1 


2 








1 


-1 


-3 


2 


—3 


-3 


-1 


1 


154 





5 


3 


2 


-2 





3 





1 


1 


-6 


_1 


1 


-1 


1 


156 


-2 


2 


-1 


-1 


1 





1 


1 





-1 


-6 


_1 





-6 


-1 


157 


4 


-2 





4 


-2 


1 


1 


2 


-2 





2 


—3 


1 


-2 


1 


160 





1 





1 


-1 





-1 


-3 


-1 


-3 


-4 




-1 


1 


1 


162 


-1 





-2 














2 


2 





-2 




2 


-1 


2 


166 


6 





3 


1 


1 








2 








-1 




1 


-2 


1 


168 


6 


3 


4 








1 





-3 


-1 


-1 


-2 




-3 


-3 


1 


169 


-8 


3 


-1 


1 





2 


1 


-3 





2 


-6 


-2 


2 


-6 


1 


172 


-2 


-8 


-5 





3 


1 





2 


1 


-2 


-2 


2 





-1 


1 


173 


2 


2 


1 





1 


-1 


-1 


1 


-1 


1 








1 


-3 





174 


-5 


7 


5 





-4 


-4 





-4 


-4 





-6 


-3 


1 


-4 


1 



